Brew: 5.1.6 Release

<!-- Release notes generated using configuration in .github/release.yml at main -->

What's Changed

• cask/artifact: enable typed: strict across Library/Homebrew/cask/artifact/ by @dduugg in https://github.com/Homebrew/brew/pull/21939
• source: retry PyPI API requests to avoid transient errors by @p-linnane in https://github.com/Homebrew/brew/pull/21944
• build(deps): bump addressable from 2.8.9 to 2.9.0 in /Library/Homebrew by @dependabot[bot] in https://github.com/Homebrew/brew/pull/21948
• build(deps): bump addressable from 2.8.9 to 2.9.0 in /docs by @dependabot[bot] in https://github.com/Homebrew/brew/pull/21949
• cask: upgrade auto_updates casks when bundle version is stale by @bevanjkay in https://github.com/Homebrew/brew/pull/21882
• refactor: remove dead code and deprecate unused public APIs by @dduugg in https://github.com/Homebrew/brew/pull/21925
• Add brew doctor and brew cleanup for corrupt Caskroom directories by @koddsson in https://github.com/Homebrew/brew/pull/21880
• refactor: remove unused require statements by @dduugg in https://github.com/Homebrew/brew/pull/21952
• cmd/*-sync: fix uninitialized constants by @cho-m in https://github.com/Homebrew/brew/pull/21956
• docs: reflect new auto_updates behaviour by @bevanjkay in https://github.com/Homebrew/brew/pull/21957
• Add 'LANG' to the environment filter to ensure it passes into brew if/when set in the user's environment by @jamesrtnz in https://github.com/Homebrew/brew/pull/21945
• docs: add and consolidate deprecation policy by @MikeMcQuaid in https://github.com/Homebrew/brew/pull/21946
• Improve updates of auto_updates casks by @MikeMcQuaid in https://github.com/Homebrew/brew/pull/21962
• search: fix uninitialized constant by @cho-m in https://github.com/Homebrew/brew/pull/21968
• bump: add cooldown for npm and PyPI by @samford in https://github.com/Homebrew/brew/pull/21888
• cask: refine auto_updates behaviour by @bevanjkay in https://github.com/Homebrew/brew/pull/21974
• generate-cask-ci-matrix: fix Linux runner for single-arch casks by @p-linnane in https://github.com/Homebrew/brew/pull/21970
• GitDownloadStrategy: fix slow repo_valid? by using -C flag by @ismail in https://github.com/Homebrew/brew/pull/21969
• build(deps): bump the github-actions group across 1 directory with 2 updates by @dependabot[bot] in https://github.com/Homebrew/brew/pull/21979
• Fix outdated greedy cask handling by @MikeMcQuaid in https://github.com/Homebrew/brew/pull/21976
• Stop cleaning corrupt cask dirs by @MikeMcQuaid in https://github.com/Homebrew/brew/pull/21980
• build(deps): bump the bundler group across 2 directories with 16 updates by @dependabot[bot] in https://github.com/Homebrew/brew/pull/21978
• Fix flaky run_actionlint! tests by @MikeMcQuaid in https://github.com/Homebrew/brew/pull/21975
• Fix flaky conflicts_with brew spec by @MikeMcQuaid in https://github.com/Homebrew/brew/pull/21977
• Share full-name parsing helpers by @MikeMcQuaid in https://github.com/Homebrew/brew/pull/21966
• Use merge-base for git audit comparisons by @MikeMcQuaid in https://github.com/Homebrew/brew/pull/21967
• docs: document developer update channel and MCP tools by @MikeMcQuaid in https://github.com/Homebrew/brew/pull/21983
• info: avoid Formula/Cask objects for counts by @MikeMcQuaid in https://github.com/Homebrew/brew/pull/21963
• sorbet: add strict type signatures to cask files by @dduugg in https://github.com/Homebrew/brew/pull/21987
• sorbet: remove redundant T.let in initialize methods by @dduugg in https://github.com/Homebrew/brew/pull/21990
• Harden cask uninstall path checks by @MikeMcQuaid in https://github.com/Homebrew/brew/pull/21989
• cask: gate auto-updates behind opt-in by @MikeMcQuaid in https://github.com/Homebrew/brew/pull/21985
• extend/os/linux/cask/config: actually use XDG_DATA_HOME by @cho-m in https://github.com/Homebrew/brew/pull/21994
• shellenv: export FPATH so child zsh shells inherit fpath by @sumanthratna in https://github.com/Homebrew/brew/pull/21910
• Add brew generate-internal-api command by @Rylan12 in https://github.com/Homebrew/brew/pull/21973
• cask/artifact/qlplugin: fix type override by @bevanjkay in https://github.com/Homebrew/brew/pull/22004

New Contributors

• @jamesrtnz made their first contribution in https://github.com/Homebrew/brew/pull/21945
• @ismail made their first contribution in https://github.com/Homebrew/brew/pull/21969
• @sumanthratna made their first contribution in https://github.com/Homebrew/brew/pull/21910

Full Changelog: https://github.com/Homebrew/brew/compare/5.1.5...5.1.6