brew services tab completion extracted the service name with awk -F'homebrew.|.service' '{print $3}'. That regex only worked for the legacy homebrew.<name> files under /opt/homebrew, where the prefix supplied the extra match. It completes nothing for the current sh.brew.<name> files, for custom service names, and for any prefix without homebrew in its path such as /usr/local or Linuxbrew.

The Bash, fish and zsh completers now take the formula name from the Cellar directory ($(NF-2) of the path) and deduplicate with sort -u, so multiple installed versions of a formula produce one entry. The generated completions are regenerated from the templates.

To reproduce: brew install postgresql@18, then brew services start and press tab. Nothing is completed before this change.

Fixes #24006

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Claude Code (Fable 5.1) drafted the implementation and tests; I reviewed the diff, verified the new test fails without the fix and passes with it, and ran brew lgtm --online plus targeted specs.