But "almost every browser" doesn't sync your saved passwords seamlessly between devices (mobile and desktop) with an end-to-end encrypted database, and automatically offer to autofill them, with the autofill itself protected by Touch ID/Face ID on the devices that support those.

For one, Bitwarden does all of that and more (I guess except the Face ID thing, but I don't really want that so I'd disable it anyway). It has web, mobile and desktop apps, and browser extensions. All available in the free plan. Oh, and it's open source and self-hostable.

https://bitwarden.com/

(Not affiliated with it, just a pretty happy (free) user!)

Neat, and glad to know about it! I've actually been surprised (and a little frustrated) that there haven't been any alternatives to iCloud Keychain for genuine seamless, e2e encrypted, password management.

Does it actually work the same as Mobile Safari's interface on iOS? Automatically presenting options both for creating and autofilling passwords on webpages? (If it can do that in iOS Firefox, I might consider it...I've been using desktop Firefox for a while because of some bizarre idiosyncratic issues I have with Safari on my laptop, that I can't reproduce anywhere else, but are extremely irritating where they do happen...)

Yes, it does. The integration with both Safari and Firefox on iOS is excellent. In Settings -> Passwords & Accounts -> Autofill Passwords you just change the backend from iCloud Keychain to Bitwarden, then it otherwise behaves substantially the same.

A big benefit of switching to Bitwarden is that you can also get it up and running on non-Apple machines. Kicking myself for not doing it earlier.

Just be aware that bulk exporting your passwords from iCloud Keychain is non-trivial.

Lastpass does this, but works with apps as well. Third party password managers are absolutely underrated, because most of them are truly cross-platform.

If you create a Netflix account on your desktop in Chrome, it can generate a password for you, or auto-grab whatever password you typed in, and will autofill that password when you open the Netflix app on your phone. (Based on a built-in association between "netflix.com" and the Netflix android app.)

Super handy feature when you get a new mobile device and need to get logged in to all your apps for the first time.

Chrome does that. If you set a passphrase for sync, then your data is e2e encrypted.

https://support.google.com/chrome/answer/165139