docs(docs): update documentation for tool installation and desktop app changes

docs/installation.mdx

@@ -23,7 +23,7 @@ The script checks the release tarball's SHA-256 before installing, as upstream d
 
 <Steps>
   <Step title="Package manager">
-    **Arch**: `sudo` for pacman. `yay` (Omarchy ships it) or `paru` is needed for AUR packages (`topgrade`, `portop`, and the desktop apps on desktop roles); without one the package script prints a warning and skips them.
+    **Arch**: `sudo` for pacman. AUR packages (`topgrade`, `portop`, and the desktop apps on desktop roles) go through `yay` or `paru`; when neither is installed the package script installs `yay` from a sync repo that ships it (CachyOS) or builds `yay-bin` from the AUR.
     **macOS**: [Homebrew](https://brew.sh) is required; the package script exits with an error if `brew` is missing.
   </Step>
   <Step title="GitHub access">
@@ -85,7 +85,7 @@ sh -c "$(curl -fsSL https://dots.prd.lk/install)" -- --version
     Configs are linked into `$HOME` (symlink mode). The neovim config and a bat syntax are cloned as externals. See [Externals and ignore rules](/chezmoi/externals-and-ignore).
   </Step>
   <Step title="Post-apply scripts">
-    gh extensions, the bat cache, the font cache, yazi plugins, and the niri user service on Linux. tpm arrives earlier as an external.
+    rustup and cargo crates, the global mise tools (`ghq`, `bun`, `node`, `uv`, `opencode`, `crush`, omp), strata on Linux desktops, then gh extensions (from a fish session), skills, the bat cache, the font cache, yazi plugins, and the systemd user services on Linux. tpm arrives earlier as an external.
   </Step>
 </Steps>