Fix: return core update checker var to main pkg - #10492

@BagToad : Thanks for opening up this draft! ✨

How I I typically test these types of changes

1. Start with the go build command that make uses and include the additional static linking done in brew formula:

   In this case, we want to build an "older version" so we can see the core CLI update behavior.

   cli/cli ‹kw/cli-10242-fix-core-github-cli-update-checker-disabled›$ rm ~/.local/state/gh/state.yml
   
   cli/cli ‹kw/cli-10242-fix-core-github-cli-update-checker-disabled›$ go build -trimpath -ldflags "-X github.com/cli/cli/v2/internal/build.Date=2025-03-06 -X github.com/cli/cli/v2/internal/build.Version=v2.67.20250306 -X main.updaterEnabled=cli/cli" -o bin/gh ./cmd/gh

2. Execute a command that gives gh long enough for the update checker to look for new releases, for example running an extension

   cli/cli ‹kw/cli-10242-fix-core-github-cli-update-checker-disabled›$ bin/gh copilot suggest
   
   Welcome to GitHub Copilot in the CLI!
   version 1.0.6 (2025-01-06)
   
   I'm powered by AI, so surprises and mistakes are possible. Make sure to verify any generated code or suggestions, and share feedback so that we can learn and improve. For more information, see https://gh.io/gh-copilot-transparency
   
   ? What kind of command can I help you with?
   > generic shell command
   
   ? What would you like the shell command to do? 
   > print hello world
   
   Suggestion:                                                                                                                                                                                                                             
                                                                                                                                                                                                                                          
     echo "Hello, World!"                                                                                                                                                                                                                  
   
   ? Select an option
   > Exit

Results of manual testing

Here is the textual version:

> Exit


A new release of gh-copilot is available: 1.0.6 → 1.1.0
https://github.com/github/gh-copilot/releases/tag/v1.1.0



A new release of copilot is available: 1.0.6 → 1.1.0
To upgrade, run: gh extension upgrade copilot
https://github.com/github/gh-copilot



A new release of gh is available: 2.67.20250306 → 2.68.1
https://github.com/cli/cli/releases/tag/v2.68.1

Here is the visual version (with long text from extension cut off)

Actually what do you think about this?

//go:build !homebrew
package updater

var Enabled = false

//go:build homebrew
package updater

var Enabled = true

Then update the homebrew build to go build --tags homebrew

This would uncouple them from the specific path. We could generalise this to --tags updatable, though I'm not sure if this is used for anything other than homebrew.

@williammartin I think that's compelling. I'll close this PR for now, and bring the discussion back to the issue, since I'll likely open a fresh PR for that implementation.