[Feature]: Run benchmarks inside CI

[abhiaagarwal]

Is your feature request related to a problem?

I've made improvements in benchmarking in #3857, #3839, and #3845. Now, we should run benchmarks in CI to make sure performance doesn't regress / track performance improvements.

Describe the solution you'd like

Use something like CodSpeed to track performance regressions over time. https://codspeed.io/docs

Describe alternatives you've considered

I'm not sure there's any other providers that are good for benchmarks, as codespeed has native support for both divan and pytest. Codspeed functions as more of a repository for benchmarks, than a benchmark runner (though they do offer specialized runners: https://codspeed.io/docs/features/macro-runners)

Priority

Low - Nice to have

Additional context

No response

Contribution

• I'm willing to submit a pull request for this feature
• I can help with testing this feature
• I can help with documentation for this feature