You might notice that your Windows installation is like 30 gigabytes and there is a huge folder somewhere in the system path called WinSXS. Microsoft bends over backwards to provide you with basically all the versions of all the shared libs ever, resulting in a system that can run programs compiled from decades ago just fine.
In Linux-land usually we just recompile all of the software from source. Sometimes it breaks because Glibc changed something. Or sometimes it breaks because (extremely rare) the kernel broke something. Linus considers breaking the userspace API one of the biggest no-nos in kernel development.
Even so, depending on what you’re doing you can have a really old binary run on your Linux computer if the conditions are right. Windows just makes that surface area of “conditions being right” much larger.
As for your phone, all the apps that get built and run for it must target some kind of specific API version (the amount of stuff you’re allowed to do is much more constrained). Android and iOS both basically provide compatibility for that stuff in a similar way that Windows does, but the story is much less chaotic than on Linux and Windows (and even macOS) where your phone app is not allowed to do that much, by comparison.
If in the future you think you might bring family/relations onboard to the password manager, it may be worthwhile to pay for a BitWarden family plan. BitWarden is really low-cost and they publish their stuff as FOSS (and therefore are worth supporting), but crucially you don’t want to be the point of technical support for when something doesn’t work for someone else. Self-hosting a password manager is an easier thing to do if you’re only doing it for yourself.
That said, I use a self-hosted Vaultwarden server as backup (i.e. I manually bring the server online and sync to my phone now and again), and my primary password manager is through Keepassxc, which is a completely separate and offline password manager program.
Edit: Forgot to mention, you can always start with free BitWarden and then export your data and delete your account if you decide to self-host.