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Second Bitwarden. Pretty cheap, good customer service. You can self-host if you prefer that route. The source code is on GitHub.

I have been using it for years. Love it.

I’m thinking of self-hosting, but can I keep using the iOS and desktop apps?

Yes, as far as I remember, you can enter the host you want to connect to in the settings.

Yes, just click on setting and type in a new URL.