feat(AvaterToken/IssueLabelToken): Migrate to CSS modules behind feature flag Pt 3

[randall-krauskopf]

Related To: https://github.com/github/primer/issues/4367

This PR is part 2 of breaking apart a larger PR into grokkable parts.

[changeset-bot]

⚠️ No Changeset found

Latest commit: ee6571b

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[github-actions]

👋 Hi, this pull request contains changes to the source code that github/github depends on. If you are GitHub staff, we recommend testing these changes with github/github using the integration workflow. Thanks!

[github-actions]

size-limit report 📦

Path	Size
packages/react/dist/browser.esm.js	98.9 KB (+0.16% 🔺)
packages/react/dist/browser.umd.js	99.21 KB (+0.04% 🔺)

[primer-integration]

👋 Hi from github/github! Your integration PR is ready: https://github.com/github/github/pull/350838

[primer-integration]

🔴 golden-jobs completed with status failure.