cmd/update: avoid switching developers to stable branch

[carlocab]

• Have you followed the guidelines in our Contributing document?
• Have you checked to ensure there aren't other open Pull Requests for the same change?
• Have you added an explanation of what your changes do and why you'd like us to include them?
• Have you written new tests for your changes? Here's an example.
• Have you successfully run brew style with your changes locally?
• Have you successfully run brew typecheck with your changes locally?
• Have you successfully run brew tests with your changes locally?

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Checking for HOMEBREW_NO_INSTALL_CLEANUP was added in #18825, but this
breaks developers by switching them to the stable branch.

Setting HOMEBREW_NO_UPDATE_CLEANUP when HOMEBREW_NO_INSTALL_CLEANUP
is set seems like a relatively recent addition, so I don't think it
hurts to just remove it. We can add it back (correctly) if there are
users that need it.