Benchmark build time of user code

Following the publication of [Scarf moving away from Haskell](https://avi.press/posts/2026-07-10-after-7-years-in-production-scarf-has-reluctantly-moved-away-from-haskell.html), discussions mentioned that type-family-heavy code, like code using beam, can build slowly.

I personally think that the tradeoff for this slower compilation is much, much more safety when interacting with the database. However, if we can preserve this safety and improve build times, we should!

This ticket is about creating a benchmark for building a beam-based application. Improvements to build times can follow separately.

No file, test, or entry point is named. Start by inspecting the repository for an existing beam-based application, benchmark, or build configuration, then measure a clean build. The work is done when it provides a repeatable build-time benchmark and a baseline for later improvements.

Written by the indexing model from the issue text.