What's a FOSS pword manager
There are probably more that these two out there but the two I know of that fit this bill are Bitwarden and KeePass. The latter comes in two flavors, the original KeePass that kinda looks like shit and tries to stay lean and defer niche features to plugins, and the fork KeePassXC that tries to give it a sleeker UX with more features natively baked-in. I will refer to both simply as "KeePass" for the rest of this comment.
that is easy to use
"Easy to use" is relative. If you're savvy enough to know what FOSS software even is, to care about using it, and to find your way onto an experimental platform like Lemmy to ask about it, I'd say youre more than capable of handling either of the above choices with ease.
reliable, likely to be around and working in 5 years
I'd wager that on both Bitwarden and KeePass.
and won't leave me feeling shit up a creek if my phone dies or I'm using a public terminal with software installation restrictions
Bitwarden offers free cloud hosting and a web interface. As long as you have access to a browser and an Internet connection, you have access to your Bitwarden key store.
KeePass is offline-only and requires specialized client software to read its key store file format. Though, since all it is is a file, you can use simple and straightforward methods to make it accessible wherever you need it. Copy it to a flash drive. SCP it between devices. Put it on a cloud service like Dropbox. You have options. It's just up to you to use them.
Bitwarden also lets you save locally stored files and manage them like KeePass, if you're into that.
Honestly, since each can be made to more or less behave like the other, which one you pick largely comes down to taste. Bitwarden is more turn-key if you want cloud hosting, KeePass makes you work for it. Bitwarden is a company providing a premium service you can buy, while KeePass is a completely free project funded only by good will donations.
I prefer KeePassXC, personally.