Automate running benchmark tests for pull requests

With the updated benchmark project in place (#7994), it would be nice to automate running this project for pull requests. This issue requires a design discussion around the right approach to do this. Some options:

1. Add a step to run the benchmarks in our existing CI pipeline
2. Use a Github Action to trigger on either a) new PRs or b) a comment such as `/benchmark `. This would also let us print the benchmark output as a PR comment in markdown which could be nice to have.

Start by reviewing the updated benchmark project in issue #7994 and the repository’s existing CI pipeline. Compare running benchmarks for every pull request with a GitHub Action triggered by a pull request or a `/benchmark ` comment. Done means the trigger, benchmark scope, and markdown output behavior have been selected and documented.

Written by the indexing model from the issue text.