You should download firefox from Mozilla site
Unpack the Firefox to your user home directory (e.g. ~/firefox)
And just run ~/firefox/firefox
You can find Firefox icon in ~/firefox/firefox/browser/chrome/icons/default/default48.png
(I recommend to use 48px size icon, but it depends)
After that you will be able update the Firefox from standard Firefox menu and you will always get fresh Firefox (in Ubuntu you can wait weeks until new release will be built).
And your Firefox will use standard Ubuntu configuration files instead of snap files.
If you need icons that displaying during Firefox running you can find them in
/usr/share/pixmaps/
and/or /usr/share/applications/
WARNING! There is may be very harsh icon cache in Ubuntu! Even if you replace some icon then the icon can be cached and old icon will be displayed. I do not know how to reset the cache.
If you use standard Ubuntu 22.04 Firefox then it will use snap and snap directories (like partial snapshot of Ubuntu system files with configurations and libraries).
You can find snap file configuration here
~/snap/
and /var/cache/snapd/
.desktop
file that you created. Please use code fences so that monospace formatting is preserved and so we can tell it apart from surrounding text. Accuracy is essential. For exampleusr\share\applications
is not a valid path but/usr/share/applications
is.