There are many red flags here, and I would jump ship immediately:
You were promised to be fast tracked to the final stage of the interview process, but then that promise was reneged on and you had to complete an additional interview stage. Make no mistake, this is reneging on a promise; it's not as simple as "circumstances have changed", this is a lie, and lies are always red flags.
You were given a task that took a week of your time. This is not normal. Usually, take-home assignments take a couple hours, or a day at most ("a day" = roughly 6 hours). Requiring you to take a task that takes a week to complete is not normal. This is fairly abusive; if the company is OK with giving you 40 hours of unpaid overtime work ("40 hours" because it took a week, and "unpaid overtime work" because you didn't get paid, and you aren't working for the company) before you even have the job, what do you think is going to happen once you're on staff?
You have to "convince him he's making a mistake". That seems very demeaning and condescending to me. You already passed their test "particularly well", and they promised to fast-track you to the final stage due to your performance (see above); the fact that you needed to further convince this person of your worth is condescending. If they don't trust the results of their test, by requiring you to further "convince" them that they are "making a mistake", then why did they waste your time with the multiple choice test in the first place? Why did they further promise to fast track you to the final interview stage? This sounds like a person who likes having power over people and playing with those he has power over, and not someone you want to work with. Any company which would keep this sort of person in a recruiting position, that speaks volumes.
The fact that, after all of the above, the company has ghosted you for 3 weeks (this behaviour is called "ghosting"), shows how important they think you are to them; you put in at least a week of your time, plus the time taken for other tests and sending emails back and forth, that they have given you. They don't respect you, and they have pretty much said as such.
Get rid of this company. While you're at it, this situation seems egregious enough that, if it was me, I would make a nasty post on their Glassdoor profile (if you are in a locale that uses Glassdoor; if not then use your local Glassdoor equivalent) and I would also name and shame them on LinkedIn. This behaviour is quite frankly despicable.
EDIT: Other answers have quoted the current COVID pandemic as a possible reason why your interview process has been stalled. In most cases, if there is a stall or hiring freeze due to COVID, the professional thing to do is to simply say so: "We respect your time and your interest, but due to the pandemic we are no longer hiring; we will get back to you if the situation changes", or something of that nature. The fact that this hasn't happened says to me that the current pandemic situation is unrelated to this recruiter treating you extremely poorly and you should not excuse them from this behaviour "due to the pandemic".
EDIT2: Side note: Your last paragraph makes no sense to me:
How big of a red flag is this? Is it like "the company is completely dysfunctional, stay the hell away from it" situation, or could it be just one bad employee, and the company is otherwise good? Do you think it's worth my time to contact the company through other channels and give it a chance?
As the saying goes, "always make a good first impression". In this case, the company's first impression is this "one bad employee". The company has the power to hire and fire their people, even their people in HR; if this person was not properly reflecting the company's values and procedures, he would have been fired or relocated. The fact that this person is who the company has chosen (I use "chosen" very specifically, this was a conscious choice by the company) to make their first impression, shows what the company's values are and how they like to be reflected. The simple fact that this person was chosen to make the company's first impression is in itself a red flag of the magnitude of "this company is completely dysfunctional, stay the hell away from it", imo.