I've had a similar situation of trying like hell to get a job with few responses.
Here's what helps me
Build a portfolio website to highlight projects and skills in more depth than a resume can. Most of my stuff is either for an employer or an attempt on my part to make a for-profit project, so I haven't included as much as I probably should. This site should include links to GitHub or other code repositories you have, sites where you have earned badges/certificates/awards/etc. for your knowledge, maybe a link to your SE/SO profile if you have a good rep on related stacks, descriptions and links to finished projects you've worked on, and anything else relevant you can think of to include. Include a link to this site in your resume, on your social media profiles, and anywhere else someone might be looking for employees.
Post a profile on LinkedIn. This should be a professional profile, not a social media profile. Post only things you want an employer to see, such as job and school history. Don't post personal pics, vacation highlights, lunch pics, or anything like that, unless your job is vacation/food critic. You don't have to be "active" on the site, just have a presence for employers to see. This link should be on your profile site and maybe on your resume. Many employers will specifically ask for a link to your LinkedIn profile. Feel free to accept friend requests from people you know, network with new people in your area of interest, and even post relevant information for other people to read, but also feel free to not accept requests from every recruiter that asks you to. Most of them aren't worth cluttering up your network.
Work on your own projects to keep your skills sharp and to prove your skills to yourself, even if you can't convince others of your worth. You can post these projects to support your online profile and will help you prove your worth. These projects work to improve your mental health, as you hit goals and make progress in the project.
Use online job searches that cater to your intended profession. I use Dice.com (as an example). I've found that other sites don't give as good search results, especially when they include jobs from other than tech industry jobs on their site. Dice isn't perfect, but you aren't going to have to wade through retail, warehousing, restaurant, and other jobs that aren't tech related. Since finding Dice, I haven't really looked for other sites. LinkedIn has their own job search, but I don't know how good it is.
Use only 1 job search site. This sounds limiting, but this helps to prevent yourself from applying to the same jobs multiple times, which can automatically disqualify you from being considered. Using one site helps keep your search simple when a recruiter directly contacts you and you think it's a duplicate of something you've already applied to.
Treat job searching as your a regular job, but don't let yourself get burnt out. This doesn't mean you do searches for 8 hours a day, but it does mean that you generally spend 8 hours trying to improve your job situation. This includes working on those personal projects that can be posted on your profile. If you can only job search 2-3 hours a day before your brain feels like it's going to explode or you get depressed, then work on those other projects for the rest of your daily allotted time. However, try to set and reach regular/normal goals before you move onto your projects. That goal could be reading through 8-10+ pages of jobs, applying to 10/20/40/more jobs, or whatever, just make sure it's realistic and that you can maintain a decent mental attitude while doing it repetitively.
Take breaks. You are only human and humans need a change of pace. We can't do the same thing forever without needing rest. Make sure you are still taking weekends, lunches, morning and afternoon (or whatever) breaks, and not killing yourself to find a job. And if you "simply can't" anymore or that whole day, then don't force yourself. Not having the energy or dreading to do something is usually your brain telling you that you are overdoing it. Believe your brain. If it keep saying the same thing for more than a couple of days, you either need to get help by talking to someone about it or you need to override your brain to see if you still "can't".
Work with temporary agencies. As L.Dutch mentioned, they have their own "bummers", but they have positives, too. They often don't include 401k, health insurance, or other normal benefits, nor do they always have holiday, PTO, or sick pay. However, they get paid based on your pay, so they will often negotiate a higher pay for you. There's also a difference between a contract and a contract-to-hire. If you want even an option to get hired after the contract ends, you'll need to stay away from a regular contract. However many end clients like to dangle a contract-to-hire to gain more interest in their jobs, but have no real interest in actually hiring anyone. Unfortunately, there's not a real good way to determine the difference between the real contract-to-hire and a fake one.
Set boundaries. If you don't want to talk to a recruiter or do an interview outside of certain hours, then don't. When you get those calls, keep it short and ask them to send you an email with more info or to call you back. If you get an email or text with a job description, ignore it until you are ready to deal with it. And if you ignore or miss one of these for over a week, feel free to contact them, but realize it might be too late. Also realize it's absolutely fine to not contact them. Recruiters "ghost" people all the time, so turnabout is fair play.
Boundaries also work for cryptic or extremely short or vague messages. If a recruiter doesn't give me enough information to actually interest me on a specific job, I don't bother contacting them back. I also look for a full job description before I agree to interview. Just like an incomplete resume will prevent you from getting an interview, incomplete information about a job will prevent an employer or recruiter from getting an interview from me.
Iffy things I do
I do some things that might not be the best idea, so I'm leaving them to last.
I use a generic cover letter that I don't change. It's specific to software development, but generic to job title and description. I include information specific to me and how I can benefit a company/employer, but generic to how it can be applied. If you are spending hours or days on a cover letter, like you say you are, you're spending far too much time that could be better used to find other jobs to apply for.
I don't apply to jobs that require me to fill out a 3rd party application. I have all my most relevant info on the 1 job search I use, so I don't feel the need to duplicate it 15 times a day or even a week.
I only sometimes do a pre-employment test/project/whatever. It depends on what they want me to do as well as how much energy/brainpower I have available. Sometimes I just can't do it, which means I need to take some time off to do "something else", anything else, to recharge my energy levels. Sometimes the project seems more like a work task they don't have time or manpower to do themselves, so since I don't work for free, I don't do it. Most times, I have no problems doing a short 1-3 hour project. If it's going to take longer than that, I have to consider how much I need or want the job, and if it's not an interesting job, I don't agree to do the project to begin with. Know your limits here, or you'll get taken advantage of.
I leave my voicemail full. If a recruiter or employer is actually interested in talking with me, they will try back or they will email me. I get dozens of emails a day for jobs and sometimes dozens of calls a day. During one 30 minute phone interview I had this past year, I had 3 people try to call me. I don't like talking on a phone, so this might be specific to me. I just don't want to spend 90% of my day on the phone, especially if it's playing phone-tag. I don't have the energy or personality to handle that. YMMV.
My last period of unemployment was this past year and lasted for 5 months. I read through nearly 2000 job descriptions and applied to over 1000 jobs across the US. This doesn't include to the likely hundreds of recruiters I talked to through email or on the phone. I had 20 interviews and ended up on my current 6 month contract. Because of the pandemic, I only applied to 100% remote positions. Because I just bought a house, I didn't apply to anything or interview at any place that required relocation.
One of the most critical things about motivation is to prevent de-motivation. Most of what I've posted here is to prevent that de-motivation. You'll need fewer motivation boosters if you de-motivate yourself less. Burnout is a huge demotivator, so my suggestions are heavily biased against burning yourself out.