Read the default browser from mimeapps.list when launching (#13520)

* Read the default browser from mimeapps.list when launching

omarchy-launch-browser and omarchy-launch-webapp asked xdg-settings for the
default browser on every launch, ~72ms through several POSIX shell scripts.
The new omarchy-cmd-default-browser reads the http handler from the
config-dir mimeapps.list files the way xdg-mime does, desktop-specific list
first, taking the first listed entry whose command is installed, in ~10ms.
With nothing set there it falls back to xdg-settings as before.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

* Let the first copy of a browser entry decide whether it is installed

A user-local entry whose browser is gone could be rescued by a system copy
of the same ID, which the launchers never read. xdg-mime judges the first
copy found, as the launchers use it, so do the same.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

---------

Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>

bin/omarchy-launch-browser

@@ -3,10 +3,7 @@
 # omarchy:summary=Launch the default browser as determined by xdg-settings.
 # omarchy:args=[url]
 
-default_browser=$(env -u BROWSER xdg-settings get default-web-browser)
-if [[ -z $default_browser ]]; then
-  default_browser=$(xdg-mime query default x-scheme-handler/https)
-fi
+default_browser=$(omarchy-cmd-default-browser)
 browser_exec=$(sed -n 's/^Exec=\([^ ]*\).*/\1/p' {~/.local,~/.nix-profile,/usr}/share/applications/$default_browser 2>/dev/null | head -1)
 
 if $browser_exec --help 2>/dev/null | grep -q MOZ_LOG; then