::Personal Opinion Warning::
When it comes to security, smoothness is kinda low on my priority list. I'm fine swapping windows to copy/paste values, or pressing a hotkey.
It's very high on my priority list. I want my employees to want to use a password manager because it's so convenient. A less perfect system that actually gets used adds more security than a more perfect system that no one likes.
There are notable advantages to browser integration - in particular not filling on spoofed "lookalike" domains made with visually similar Unicode characters, and not putting passwords into the clipboard where they might be snagged by anything watching the clipboard.
(admittedly, if your system has something malicious monitoring clipboard use you already have big problems)
Lack of smoothness is what causes many people to ignore these things. So, while you or I may know better, its still a very important aspect if we want more than just the few in the know people to use security tools.
I have also used multiple shared Keepass files at work and the issue isn't a lack of smoothness. There have been multiple instances of sync/dataloss issues where you have to refer to an old version or find someone who has the latest "OK" version of the file.
I love Keepass for personal use, but if you using it for sharing passwords at work then 1Password or Bitwarden are the way to go.
I'm using KeePass + Syncthing to get it around all my devices. Works like a charm! Except for iOS devices...
At work we share a Keepass file on a nextcloud instance and it's a giant PITA.