brew.sh: add bump to HOMEBREW_NO_INSTALL_FROM_API commands

[carlocab]

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---

brew bump relies on livecheck, which we don't want to query the API
for.

Also, some small refactoring:

1. Declare the list of commands we want to set
   HOMEBREW_NO_INSTALL_FROM_API for as an array.
2. Only check against this list when the command being run is a
   developer command, to avoid checking the list when we know we're not
   running a dev command.

[BrewTestBot]

Review period will end on 2023-02-08 at 06:38:11 UTC.

[Rylan12]

Thanks, looks good to me!

[BrewTestBot]

Review period skipped due to critical label.

[MikeMcQuaid]

Thanks @carlocab!

• Declare the list of commands we want to set
  HOMEBREW_NO_INSTALL_FROM_API for as an array.

Good idea! May want to do the same for https://github.com/carlocab/brew/blob/76466f66d26ef721186fcf2b555616db979f2861/Library/Homebrew/brew.sh#L240

[carlocab]

Good idea! May want to do the same for https://github.com/carlocab/brew/blob/76466f66d26ef721186fcf2b555616db979f2861/Library/Homebrew/brew.sh#L240

#14554