the zsh snippet in the README only works with zsh's built-in git completion — but Homebrew's git ships its own _git wrapper that shadows the built-in and never defines __git_branch_names, so branch <tab> fails for anyone with brew git.

also, $(brew --prefix)/share/zsh/functions doesn't exist unless zsh itself came from brew, and autoload -Uz _git && _git errors at shell startup.

so:

• replace with a compdef _git_friendly branch=git-checkout approach that works with both the built-in completion and git's wrapper (verified by scripted tab-presses in both configs)
• merge <tab> now completes too, matching the bash instructions

to test: add the new snippet to your .zshrc after compinit, rm -f ~/.zcompdump*; exec zsh, then branch <tab> in any repo