Let any installed browser be the default, Flatpaks included

[28allday]

Problem

Setup > Defaults > Browser is a fixed list of seven browsers. A browser installed any other way (Flatpak, AUR, a hand-written desktop entry) shows up in the app launcher but has no route to becoming the default, and omarchy default browser only accepts the seven names.

Flatpak browsers fail a second way: omarchy-launch-browser and omarchy-launch-webapp only look for the desktop entry under ~/.local, the Nix profile and /usr, and take the first word of Exec as the command. A Flatpak entry lives under Flatpak's exported data dir and its Exec is a whole flatpak run --command=... app.id @@u %u @@ line, so even after setting it with xdg-settings by hand, Super + Shift + Return does nothing.

Change

• Other row at the bottom of Defaults > Browser. It opens a picker listing every installed desktop entry that handles x-scheme-handler/https, wherever it came from, marks the current default, and hands the chosen desktop id to omarchy-default-browser. The row shows ✓ whenever the default is something outside the built-in seven.
• omarchy default browser <desktop-id> sets any existing entry as the default (nothing to install on its behalf, so an unknown id is refused rather than opening an installer). The seven named browsers behave exactly as before.
• New hidden helper omarchy-cmd-desktop-entry resolves an entry through XDG_DATA_HOME / XDG_DATA_DIRS (plus the Nix profile and Flatpak export dirs) and returns its Exec with field codes and Flatpak's @@u/@@ markers stripped. The browser launcher and web-app launcher use it, so Flatpak browsers launch, get the right private-window flag, and are focused by app id rather than by "flatpak".
• Web apps recognise the Flatpak ids of the Chromium-family browsers (org.chromium.Chromium, com.brave.Browser, ...) instead of falling back to native Chromium.
• Manual page for browsers updated.

Tests

• New default-browser-any-test.sh: entry resolution across data dirs (user dir wins, Flatpak export dir found), field-code stripping, setting a default by desktop id, refusing an unknown id, and the picker's listing (Flatpak entry present, shadowed entry listed once, NoDisplay and non-browser handlers skipped).
• launch-browser-test.sh gains a Flatpak browser case: full flatpak run command passed through, markers stripped, window focused by app id.
• menu-test.sh expects the new Other row.

test/shell passes apart from failures already present on quattro that this change does not touch (bin-style on omarchy-remove-ai-openclaw, bar-icon-geometry, and the three tests that need an omarchy-pkgs sibling checkout).