chore: Update rust-cache and add it to more jobs

[MichaReiser]

Summary

• Uses the clippy action that comments on the PR (falls back to a message in STDOUT for non-core members)
• Updates the rust cache from version 1 to 2
• Uses specific cache keys to make better use of our caches: GitHub only supports storing 10GB of caches which we easily exceed if we cache the dependencies for each job (~500mb per job)
• Adds the caches to more jobs like building wasm etc.
• Changes the order of Clippy and cargo check --release to first run clippy as this is the command that is more likely to fail (we only run cargo check` to detect issues specific to release builds)
• Use nextest to run unit test (continues to use cargo test for doctest as doctests aren't supported by nextest yet)

Test Plan

I verified that the PR and bench workflows only rebuild the rome crates (the action only caches dependencies). We'll have to land the PR to test the changes to the main workflow.

• Check JS: 7m 30 -> 5m 30
• Typecheck JS: 7m 20 -> 5m
• Lint rust files 13m -> 5m
• Documentation 5m -> 2m
• Codegen 5m -> 2m 30

[netlify]

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[MichaReiser]

!bench_formatter

[calibre-analytics]

Comparing chore: Update rust-cache and add it to more jobs Snapshot #5 to median since last deploy of rome.tools.

	LCP?	CLS?	TBT?
Overall Median across all pages and test profiles	2.41s  from 257ms	0.0 no change	124ms no change
Chrome Desktop Chrome Desktop • Cable	2.41s  from 257ms	0.0 no change	349ms  from 19ms
iPhone, 4G LTE iPhone 12 • 4G LTE	1.04s  from 243ms	0.0 no change	5ms no change
Motorola Moto G Power, 3G connection Motorola Moto G Power • Regular 3G	16.3s  from 1.07s	0.0 no change	124ms no change

1 page tested

 Home

Browser previews

Chrome Desktop	iPhone, 4G LTE	Motorola Moto G Power, 3G connection

Most significant changes

	Value	Budget
JS Parse & Compile Motorola Moto G Power, 3G connection	1.61s  from 25ms
Total JavaScript Size in Bytes Chrome Desktop	5.36 MB  from 86.8 KB
Total JavaScript Size in Bytes iPhone, 4G LTE	5.36 MB  from 86.8 KB
Total JavaScript Size in Bytes Motorola Moto G Power, 3G connection	5.36 MB  from 86.8 KB
JS Parse & Compile iPhone, 4G LTE	492ms  from 11ms

_{27 other significant changes: JS Parse & Compile on Chrome Desktop, Total Blocking Time on Chrome Desktop, Largest Contentful Paint on Motorola Moto G Power, 3G connection, First Contentful Paint on Motorola Moto G Power, 3G connection, Total CSS Size in Bytes on Chrome Desktop, Total CSS Size in Bytes on iPhone, 4G LTE, Total CSS Size in Bytes on Motorola Moto G Power, 3G connection, Total Page Size in Bytes on Chrome Desktop, Total Page Size in Bytes on iPhone, 4G LTE, Total Page Size in Bytes on Motorola Moto G Power, 3G connection, Time to Interactive on Motorola Moto G Power, 3G connection, Largest Contentful Paint on Chrome Desktop, First Contentful Paint on Chrome Desktop, Time to Interactive on Chrome Desktop, Number of Requests on Motorola Moto G Power, 3G connection, Number of Requests on Chrome Desktop, Number of Requests on iPhone, 4G LTE, Speed Index on Motorola Moto G Power, 3G connection, Time to Interactive on iPhone, 4G LTE, First Contentful Paint on iPhone, 4G LTE, Largest Contentful Paint on iPhone, 4G LTE, Speed Index on Chrome Desktop, Total HTML Size in Bytes on Chrome Desktop, Total HTML Size in Bytes on iPhone, 4G LTE, Total HTML Size in Bytes on Motorola Moto G Power, 3G connection, Lighthouse Performance Score on Motorola Moto G Power, 3G connection, Lighthouse Performance Score on Chrome Desktop}

_{Calibre: Site dashboard | View this PR | Edit settings | View documentation}