alt Hacker NewsDepends on what qualifies as a password "manager", but I've been using pass (https://www.passwordstore.org/) for years on multiple desktops, and have recently added iOS app sepass to my setup (https://sepass.modiot.com/).
Quite complicated to get it all setup (definitely not for non-technical users), but both are GPL and I now have all my passwords available with hardware protection (yubikey on desktop, secure enclave on iOS) in all locations.
It doesn't even have to be something as bare-bones as pass. You can have a full-fledged password manager that is open-source and local-first. KeepassXC (and the OG Keepass) were always OSS and local-first. The original version of Keepass 1.0 for Windows was released long before Lastpass or 1Password[1], so we had an open-source local-first password manager before we had commercial cloud-based managers.
[1] To be more accurate, although it was always proprietary, 1Password was also local-only at first, with syncing only supported by putting it on something like Dropbox. They only added native cloud syncing later and eventually made it cloud-first.