There are two reasons that your companies policies right now are illegal:
For one, right now, it is the law to enable personnel to work from home whenever possible. And everybody else working remotely is strong evidence that it is indeed possible.
But generally speaking, as an apprentice in Germany you cannot work in conditions that the other apprentices in your profession and actual professionals in your company do not have to work under. For example you cannot be required to clean the kitchen. You can be required to clean the kitchen if the other full time employees doing the job you are being trained for have to do it too. So for example everybody does it once a week and at some point it's your turn. That's fine. Saying the Azubi has to do so the others can do their work without disruptions is illegal.
Remote work is a working condition. Working conditions are not separable from your actual work. It is obviously just as illegal to have everybody work on a desk in the first floor office, and just the Azubis working in the basement next to the open sewer.
Please note that perks for seniority do not apply to this concept. So if seniors get a company car (or an office with A/C) and juniors don't, it is perfectly fine to treat apprentices as juniors, after all that is the job the would have if they finished their apprenticeship. But as I understood you, their take is that everybody can do remote work, except Azubis. That is illegal.
So denying you remote work while everybody else is working from home, is illegal even twice. This is not a perk you don't get or an unfairness you have to live with. It's illegal. Period.
Given that Azubis do not make enough money to live on their own without support, it is very likely that your trip to the office consists of risky mass transit usage compared to your leaderships relatively safe drive in their own private vehicle and you are sitting in a bigger, shared office while they have their own room to close the doors, open the windows or disinfect whatever and whenever they feel like. So even if they would say "I'm in the office, why can't you." it would be quite hypocritical.
Is there anything I can do to lessen the tension between me and the companies leading staff members and get at least a few days of home office?
Well, here is the problem. Your company’s leadership consists of self-absorbed idiots. You could show them the laws, but neither of them will convince them they are wrong. Not the general apprenticeship laws, not the current specific COVID regulations. It's not like after 2 years of your apprenticeship and one full year of COVID, they somehow have not heard how this stuff works. They know and they don't give a shit.
You might ask your local IHK for tips and even for a moderator to help in conflicts. They will tell your company exactly what I told you. But we already established your bosses are idiots and telling an idiot they are wrong only angers them.
So do you want to anger your boss? That is a personal decision that is up to you.
Normally, I would caution you. If this were about a perk, I would say you should not stir up bad feelings, instead keep your head down, finish your apprenticeship, stay there for a few months and then look for another company. Because "übernommen werden" looks good on your CV, and finishing your apprenticeship at all is self-explanatory.
But this is not about a perk. Or a little unfairness on the job that is temporary at best. This is about your life. We don't do remote work to be able to have an easier lunch break. We do this because there is a potentially deadly disease out there. Risking your good relationship with your boss for a temporary perk is not worth it, but lets put it this way:
Your boss does not trust you enough to let you work from home. Your boss does not value you enough to allow basic measures of protecting your own health. You have no "good relationship" with your boss. If you had one, this thread would not exist. Your boss is violating health regulations and labor laws and is enough of a hypocrite to not even do it for all their workers, no, only for you. There is no "good relationship" to safe or salvage.
So talk to your "Ausbilder" in the company first. They should help you. Chances are they are leadership in your company and already aware, so the next step is talk to the IHK. Give them a call. Make it urgent. Your health is urgent. If they cannot or will not help, ask a lawyer.
Yes, this is the nuclear option and it will make your boss mad. But again, they are an hypocritical, egoistic idiot, there is no way to enforce the law and make them happy.
There is multiple bad outcomes, but if you had the choice whether to come down with COVID and be liked by your boss (where "like" means being subject to multiple labor law violations) or be hated by your boss, but generally healthy, I don't think that is a hard decision.