Are you aware that you've been running a version that hasn't been getting updates since July of last year? If not, then having your OS actually get updates again might be a surprise. You'll have to update to 20.04 first, though, and then 20.10 before you can update that to 21.04. There's no direct update path (another known surprise, one might say). If you don't want to update every six months, just stick to the long-term support version (LTS, currently 20.04).

The bootloader was broken for this laptop model in 19.10 and I've been deferring going through the same pain upgrading to 20.04. Totally aware of the support situation and upgrade sequence, but an unsupported machine sure beats a bricked machine

You should definitely go to the pain of upgrading to 21.04, since xx.04 releases get updates for 5 years instead of 6 months.

21.04 is not an LTS with 5 years of support. The latest LTS is 20.04.

True:

Ubuntu 21.04 will be supported for 9 months until January 2022. If you need Long Term Support, it is recommended you use Ubuntu 20.04 LTS instead.

Only every second xx.04, to the best of my knowledge. 20.04 was an LTS release, the next LTS will be 22.04. 21.04 is a standard release supported for 6 months.

Edit: Ninja'd by jpace121, should have refreshed before commenting.

Even if my machine won't boot afterwards?

You'll never have to upgrade it again!

Not too many, as it has been EOL since July 2020.

Why 19.10? (I mean, why not 20.04 lts?)

Because I'm running it of course.

I don't run Ubuntu. If I did, your question has convinced me I would be happiest on an LTS version. 5 years of not changing much is more in line with my level of interest in puttering around my OS settings than every 9 months.

https://ubuntu.com/about/release-cycle

The 19.10 bump was to get some fresh base libraries to build something as I recall. I think it might have for Remmina. Otherwise totally agree with you, LTS is always preferable