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If you’re brave enough to roll your own: KeePass XC. If not, Bitwarden. (edit for clarity)
That’s not hosting, it’s just a local file.
If you want to access your KeePass safe from multiple devices (phone, tablet, PC, etc), you have to host it somewhere.
You can put it on Google drive or something similar. You could also use syncthing (like how I do it) and you still don’t have to host anything.
or just sync the file using syncthing or plain old rsync?