Reduce install command load time

[MikeMcQuaid]

• Split lightweight formula checks and the base cask class from their larger implementation graphs.
• Load full formula and cask installers only when their paths are used.
• Cut warm no-op command_load from 96.96ms to 53.95ms on this base.

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• Have you followed our Contributing guidelines?
• Have you checked for other open Pull Requests for the same change?
• Have you explained what your changes do? Performance claims (e.g. "this is faster") must include Hyperfine benchmarks.
• Have you explained why you'd like these changes included, not just what they do?
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• Have you written new tests (excluding integration tests)? Here's an example.
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• I did not use AI/LLM to create this PR, or I disclosed the tool/model below and reviewed its output; I did not attribute commits to AI and will answer maintainer questions and review comments myself without AI/LLM.

GPT 5.6 Sol xhigh with local review and testing.

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[Copilot]

Pull request overview

This PR reduces brew install command load time by splitting lightweight install checks and the cask base class out of heavier require graphs, and by deferring full installer/cask implementation loads until the relevant code paths execute.

Changes:

• Extracted Install.install_formula? into a new lightweight Library/Homebrew/install/check.rb and updated call sites to require it early.
• Introduced Library/Homebrew/cask/cask_base.rb and updated livecheck.rb to depend on the lightweight base instead of requiring the full cask implementation.
• Deferred heavyweight requires in cmd/install.rb, cli/named_args.rb, and cleanup.rb, and added a spec to assert deferred loading at command load time.

Reviewed changes

Copilot reviewed 9 out of 9 changed files in this pull request and generated 1 comment.

Show a summary per file

File	Description
Library/Homebrew/test/cmd/install_spec.rb	Adds a command-load regression test for deferred requires; updates test requires accordingly.
Library/Homebrew/livecheck.rb	Uses cask/cask_base to avoid pulling in the full cask graph at load time.
Library/Homebrew/install/check.rb	New lightweight module containing Install.install_formula? pre-install checks.
Library/Homebrew/install.rb	Requires install/check and removes the inlined install_formula? implementation.
Library/Homebrew/cmd/install.rb	Defers heavy requires (install, cask installer/upgrade, attestation, missing_formula) to runtime paths.
Library/Homebrew/cli/named_args.rb	Defers cask/cask_loader until actually needed for cask loading/conflict warnings.
Library/Homebrew/cleanup.rb	Defers cask/cask_loader until clean! execution.
Library/Homebrew/cask/cask.rb	Requires cask/cask_base and relies on it for Forwardable extension.
Library/Homebrew/cask/cask_base.rb	New minimal Cask::Cask base to support lightweight type references and later reopening.

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