There is a lot to unpack here and I'm going to try to break it into parts. At the moment you are objecting to
- preparing and delivering a 5 minute talk on some software you don't sound very proud of and don't appear to believe is important to the company (Even though you've been able to work on it when your supervisor would prefer you do something else.)
- travelling half a day somewhere and half a day back, out of working hours, in Covid-unsafe conditions.
- listening to a day's worth of 5 minute talks from your colleagues on topics you know nothing about but are sure are worthless.
You are being asked to engage, to show you care about this company and feel connected to it. You are being offered a chance to show others in the firm (some of whom could be your future peers or supervisors) what good and important work you do. You are being offered a chance to see what else is going on all over the company, things you might in fact want to be part of.
If it wasn't for the dangerous and unpaid travel I would urge you to do this and tell you why it could be so good for you. But the "buy yourself a train ticket or whatever" part of this is weird. Really weird.
If you truly think your job is on the line, try this. Ask (in email, to your supervisor and ccing someone else who cares, like the person you've been interacting with for this project or the person who invited you to speak, pretty much anyone) for the following arrangement: the company will cover your train tickets and two hotel nights. You will travel during the workday the day before the event (if that's a Sunday, you'll get a day off in lieu of your Sunday later), arriving at close of day, spend the night, attend the event the next day, spend another night, and travel home during the workday the next day. (If that's a Saturday, you'll get a day off for it later.) Further, you'll need some freedom to choose uncrowded train times. I know this means a lot of time away from family, and unpaid time sitting around in a hotel watching TV, but that is what happens when you travel on business.
Are they likely to agree to this for a 5 minute talk? No. But if that's what you really need in order to do it, ask for what you need. (Side effect: if they do agree, you'll know they really do value it, and you.) Are they likely to fire you for asking? Possibly, it is a lot to ask and implies you value yourself a lot more than they value you. That's probably true though, and it's why I recommend this only if you think you're likely about to be fired if you don't go. And since they probably won't agree, you can then offer to do it remotely as a backup plan. At no time will you mention that you think the talks are pointless or that you don't want to listen to the other ones, that the project isn't worth presenting on or anything like that. You will adopt a position of "thankyou for the opportunity to demonstrate the great work I did on this project" and you are simply clarifying what is needed for you to be able to do that.
If they can't make your travel feel less unfair and dangerous, and they won't set up a remote talk, then -- and this is advice you'll need other times too -- do not refuse. What you are going to do is decline this lovely opportunity that they have been so nice as to give you. Seriously, I mean it. You think it's great that people can talk about their projects, and you would enjoy hearing about other people's projects, but unfortunately you're just unable to accept that generous offer this year.
I have a client who holds an annual get together. I am not paid for my time if I go to it. Some years, I go. I think it's worth it. Some years, I don't. When I don't, I never refuse, I decline. They don't hold it against me. Your employer may be different. But I think the tension you're feeling from your employer is related more to your reluctance to engage with the firm as a whole than it is to your opinions on travel at the moment. See how much of that you can fix.