Password managers are very different. The details get encrypted using a passphrase, and only the encrypted data gets sent to the password manager. You don't have to trust the backend unless the frontend is changed to send non-encrypted data and/or your passphrase.
I use KeepassXC and synchronize the encrypted database across my devices using my own Nextcloud instance. But even if I used a mainstream cloud provider, that wouldn't matter since the db is encrypted and decrypted locally.
Regarding trusting the frontend, in my case I just need to check that KeepassXC itself isn't sending data around. Which I admit I didn't do so far, but in my view the alternative of reusing password is much more likely to get you in trouble compared to the likelihood of KeepassXC sending your data to a tird party without anyone noticing.
Yes but, depending on how the ecosystem is built, the amount of trust needed can be smaller or greater. Reality isn't black or white, we also have shades and colors.
Of course. I'd just rather trust many people narrowly rather than trusting a few people with everything. And the people who can push updates to password manager front ends... we're trusting them with everything. It's a situation which calls for a bit of extra diligence.