>Password managers are those proprietary programs that you need to install, give full access to your computer, register an account and trust their word that your passwords are uploaded to the cloud securely? No thanks.

cf. pass(1)[0][1]

[0] https://www.passwordstore.org/

[1] No, it's not hosted in the cloud (i.e., on someone else's servers) and that's a good thing. It's FOSS and can be compiled for Android/IOS (and has, see [2][3][4], least for Android). The DB (just a GPG store) can also be shared across multiple devices.

[2] https://f-droid.org/packages/app.passwordstore.agrahn/

[3] https://play.google.com/store/apps/details?id=dev.msfjarvis....

[4] Not sure about IOS versions, I don't have any Apple devices.