I've thought about doing this as well, but I really like the password manager integration in Firefox. How does the Keepass Browser Extension work? Is it as seamless and do you need to have Keepass running in the background at all times?
You have to pair the add-on with the KeepassXC program once. Whenever you visit websites that you have saved passwords for, you are asked (via popup) if you want the add-on to fetch the login name and password (because it can handle multiple login combinations for the same websites). Then you have a second click on a small symbol next to the login form which then actually fills in your login data.