[WIP] Fix deprecation of conflicts_with formula in autoupdating casks

[Copilot]

Thanks for assigning this issue to me. I'm starting to work on it and will keep this PR's description up to date as I form a plan and make progress.

Original prompt

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This section details on the original issue you should resolve

<issue_title>Deprecation of conflicts_with formula is causing errors from previously installed autoupdating casks</issue_title>
<issue_description>### brew doctor output

❯ brew doctor
Your system is ready to brew.

Verification

• I ran brew update twice and am still able to reproduce my issue.
• My "brew doctor output" above says Your system is ready to brew or a definitely unrelated Tier message.
• This issue's title and/or description do not reference a single formula e.g. brew install wget. If they do, open an issue at https://github.com/Homebrew/homebrew-core/issues/new/choose instead.

brew config output

❯ brew config
HOMEBREW_VERSION: 4.6.7-21-gaf6f648
ORIGIN: https://github.com/Homebrew/brew
HEAD: af6f648f00f424b510680821b7f2b50af7e4315e
Last commit: 3 hours ago
Branch: main
Core tap HEAD: 32b0299f1cfff1eb7142623f782d44aa69c0673b
Core tap last commit: 2 days ago
Core tap JSON: 25 Aug 21:24 UTC
Core cask tap HEAD: 847338de059cc9a545250d7942e9950c1ddc3040
Core cask tap last commit: 2 days ago
Core cask tap JSON: 25 Aug 21:24 UTC
HOMEBREW_PREFIX: /opt/homebrew
HOMEBREW_CASK_OPTS: []
HOMEBREW_FORBID_PACKAGES_FROM_PATHS: set
HOMEBREW_MAKE_JOBS: 8
HOMEBREW_NO_EMOJI: set
HOMEBREW_SORBET_RUNTIME: set
Homebrew Ruby: 3.4.5 => /opt/homebrew/Library/Homebrew/vendor/portable-ruby/3.4.5/bin/ruby
CPU: octa-core 64-bit arm_firestorm_icestorm
Clang: 17.0.0 build 1700
Git: 2.51.0 => /opt/homebrew/bin/git
Curl: 8.7.1 => /usr/bin/curl
macOS: 15.6.1-arm64
CLT: 16.4.0.0.1.1747106510
Xcode: 16.4 => /Applications/Xcode-16.4.0.app/Contents/Developer
Rosetta 2: false

What were you trying to do (and why)?

Run any kind of brew command that updates homebrew

What happened (include all command output)?

Since #20499 landed any time homebrew does an autoupdate, I'd get the following message repeated in the output:

Warning: Calling conflicts_with formula: is deprecated! There is no replacement.

For example, here is the complete output from an install command I ran this morning:

❯ brew install webkit2png
==> Auto-updating Homebrew...
Adjust how often this is run with `$HOMEBREW_AUTO_UPDATE_SECS` or disable with
`$HOMEBREW_NO_AUTO_UPDATE=1`. Hide these hints with `$HOMEBREW_NO_ENV_HINTS=1` (see `man brew`).
==> Auto-updated Homebrew!
==> Updated Homebrew from 4.6.6 (566290dcbc) to 4.6.7 (af6f648f00).
Updated 2 taps (homebrew/core and homebrew/cask).
==> New Formulae
bunster: Compile shell scripts to static binaries
ggc: Modern Git CLI
gtrash: Featureful Trash CLI manager: alternative to rm and trash-cli
mac-cleanup-py: Python cleanup script for macOS
melt: Backup and restore Ed25519 SSH keys with seed words
nifi-toolkit: Command-line utilities to setup and support NiFi
podcast-archiver: Archive all episodes from your favorite podcasts
protozero: Minimalist protocol buffer decoder and encoder in C++
typtea: Minimal terminal-based typing speed tester
wishlist: Single entrypoint for multiple SSH endpoints
[email protected]: Programming language designed for robustness, optimality, and clarity
==> New Casks
orcaslicer@nightly: G-code generator for 3D printers
petrichor: Offline Music Player

You have 1 outdated formula installed.
Warning: Calling conflicts_with formula: is deprecated! There is no replacement.
Warning: Calling conflicts_with formula: is deprecated! There is no replacement.


The 4.6.7 changelog can be found at:
  https://github.com/Homebrew/brew/releases/tag/4.6.7
==> Fetching downloads for: webkit2png
Warning: webkit2png has been deprecated because it is not supported upstream! It will be disabled on 2026-03-21.
==> Downloading https://ghcr.io/v2/homebrew/core/webkit2png/manifests/0.7
############################################################################################################################################################ 100.0%
==> Fetching webkit2png
==> Downloading https://ghcr.io/v2/homebrew/core/webkit2png/blobs/sha256:ad209d841f88f9b5d3a969e2493d853237c89234bd09dfc3d1aa2106832d2d7d
############################################################################################################################################################ 100.0%
==> Pouring webkit2png--0.7.all.bottle.tar.gz
/opt/homebrew/Cellar/webkit2png/0.7: 5 files, 23KB
==> Running `brew cleanup webkit2png`...
Disable this behaviour by setting `HOMEBREW_NO_INSTALL_CLEANUP=1`.
Hide these hints with `HOMEBREW_NO_ENV_HINTS=1` (see `man brew`).
==> No outdated dependents to upgrade!

What did you expect to happen?

I didn't expect any error messages, not least because none of the taps I have installed call the deprecated method:

❯ cd /opt/homebrew/Library/Taps
❯ grep -r conflicts_with * | grep formula
homebrew/homebrew-core/Formula/b/bash-completion.rb:  conflicts_with "bash-completion@2", because: "each are different versions of the same formula"
homebrew/h...

</details>



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- Fixes Homebrew/brew#20575

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