As long as you don't run Gentoo or any other distro that require you to compile your own packages, you can install the Firefox from repos and you'll have the same result.

I really suggest you to use yours distro package manager to install Firefox and use KeePassXC as flatpak, cause this way you'll have your apps updated.

Your solution, despite works, you'll have to update the packages by hand

However be aware that Ubuntu force you to install Firefox Snap even if you run apt install firefox, so you'll face the same issue. For this reason I suggest you to move away from Ubuntu

In my opinion, the web browser is the single most important application that should be sandboxed on a system. We use them to access nearly everything on the Internet, including resources that are routinely laden with obfuscated JavaScript.

Every attempt should be made to separate the browser from the host system, and circumventing that safeguard in order to facilitate direct access to your password database is risky at best.

Edit: I don't mean to suggest that I have the perfect solution either, but I keep everything sandboxed and just opt for KeePassXC's native global hotkey for auto-filling credentials.

This solution is outdated and complex.

I suggest you to have your Firefox as a native installation and you can keep KeepassXC as flatpak.

It may work out of the box