How to prevent _brew_ from updating itself?

[dseight]

Output of brew config

HOMEBREW_VERSION: 4.4.15-70-g1e91082
ORIGIN: https://github.com/Homebrew/brew
HEAD: 1e91082d67661715656915372a6a7d9b1868668e
Last commit: 2 days ago
Branch: HEAD
Core tap HEAD: 62957dd2f405f48a82046b056ada9a95f9043e6b
Core tap last commit: 2 hours ago
Core tap JSON: 12 Jan 15:48 UTC
Core cask tap HEAD: d3523a64c6a7327c148783757905ba2a3101cba8
Core cask tap last commit: 89 minutes ago
Core cask tap JSON: 12 Jan 15:48 UTC
HOMEBREW_PREFIX: /opt/homebrew
HOMEBREW_CASK_OPTS: []
HOMEBREW_EDITOR: nvim
HOMEBREW_MAKE_JOBS: 10
HOMEBREW_NO_AUTO_UPDATE: set
HOMEBREW_SORBET_RUNTIME: set
Homebrew Ruby: 3.3.6 => /opt/homebrew/Library/Homebrew/vendor/portable-ruby/3.3.6/bin/ruby
CPU: 10-core 64-bit arm_firestorm_icestorm
Clang: 16.0.0 build 1600
Git: 2.44.0 => /opt/homebrew/bin/git
Curl: 8.7.1 => /usr/bin/curl
macOS: 15.2-arm64
CLT: 16.2.0.0.1.1733547573
Xcode: 16.2
Rosetta 2: false

Output of brew doctor

Your system is ready to brew.

Description of issue

Hi! I'm aware that it's possible to disable auto-updates of taps by setting HOMEBREW_NO_AUTO_UPDATE to 1, but how can I prevent the brew executable from updating itself if not explicitly asked to?

I.e. here I want only taps to be updated, but getting brew updated:

$ brew update
==> Updating Homebrew...
==> Updated Homebrew from 4.4.8 (60890774e0) to 4.4.15 (1e91082d67).
No changes to formulae or casks.

The 4.4.15 changelog can be found at:
  https://github.com/Homebrew/brew/releases/tag/4.4.15

I tried setting SKIP_FETCH_BREW_REPOSITORY to 1, but that didn't helped.

[p-linnane]

This is not something we support.

[xer0x]

Nix-darwin might do this by removing the git remotes

[p-linnane]

This is a bad idea. We are a rolling release package manager. Using old versions of brew is a surefire way to run into a bunch of strange issues, and we will not provide any official support for it.