fix(desktop): apply the configured cursor theme to the Hyprland session

home.sessionVariables (XCURSOR_THEME/XCURSOR_SIZE from home.pointerCursor)
land in hm-session-vars.sh, which only a login shell sources. UWSM starts
the graphical session without it, so Hyprland never saw the theme and drew
its built-in cursor instead of the configured Bibata-Modern-Ice.

Declare the cursor through Hyprland's own env directive, read at compositor
startup regardless of the shell profile, sourced from config.stylix.cursor
so the theme and size stay defined in one place.

CLAUDE.md

@@ -109,3 +109,8 @@ The domain model (Host, Module, Skeleton, Auto-loader, Enable convention, overla
   To actually remove a builtin, list it explicitly with `<engine>.metaData.hidden = true` — an engine entry carrying only `metaData` is treated as a builtin rather than a custom engine.
   Engines are referenced by their current id, which the module maps from the old display names, so the default is `default = "ddg"`, not `"DuckDuckGo"` (the latter only warns and migrates).
   Prove the result by decoding the built file: `mozlz4a -d <search.json.mozlz4>` shows the `_metaData.hidden` flags and `defaultEngineId`.
+- `home.sessionVariables` do **not** reach the Hyprland session, so anything the compositor reads from its environment (cursor theme, toolkit hints) has to be declared elsewhere.
+  home-manager writes those variables to `hm-session-vars.sh`, which only a login shell sources; UWSM starts the graphical session without it, so the compositor's environment never gains them.
+  This is why a Stylix cursor (`XCURSOR_THEME`/`XCURSOR_SIZE` via `home.pointerCursor`) silently fails to apply and Hyprland draws its built-in cursor: the variables exist in `sessionVariables` but not in the running session (`tr '\0' '\n' < /proc/$(pgrep -x Hyprland)/environ` shows them absent).
+  The fix is Hyprland's own `env = KEY,VALUE` directive in `settings`, read at compositor startup regardless of the shell profile; `modules/desktop/hyprland/hyprland.nix` sets the cursor that way, sourced from `config.stylix.cursor`.
+  Bibata ships XCursor format only (no `hyprcursor/` dir), which Hyprland renders through its XCursor fallback, so both `XCURSOR_*` and `HYPRCURSOR_*` naming the same theme are safe.