Restyle RPC: Refactor to share common code between examples

[restyled-io]

A duplicate of #9444 with additional commits that automatically address
incorrect style, created by Restyled.

⚠️ Even though this PR is not a Fork, it contains outside contributions.
Please review accordingly.

Since the original Pull Request was opened as a fork in a contributor's
repository, we are unable to create a Pull Request branching from it with only
the style fixes.

The following Restylers made fixes:

• gn

To incorporate these changes, you can either:

1. Merge this Pull Request instead of the original, or

2. Ask your contributor to locally incorporate these commits and push them to
   the original Pull Request

   Expand for example instructions

   ```console
   git remote add upstream https://github.com/project-chip/connectedhomeip.git
   git fetch upstream pull/<this PR number>/head
   git merge --ff-only FETCH_HEAD
   git push
   ```
   

NOTE: As work continues on the original Pull Request, this process will
re-run and update (force-push) this Pull Request with updated style fixes as
necessary. If the style is fixed manually at any point (i.e. this process finds
no fixes to make), this Pull Request will be closed automatically.

Sorry if this was unexpected. To disable it, see our documentation.