ci: script and workflow to update starter projects

[jordanrfrazier]

Adds a workflow to update and autofix the starter projects.

[codspeed-hq]

CodSpeed Performance Report

Merging #5195 will degrade performances by 67.32%

_{Comparing script-update-starter-projects (788945b) with main (3f9dab9)}

Summary

❌ 3 regressions
✅ 12 untouched benchmarks

⚠️ Please fix the performance issues or acknowledge them on CodSpeed.

Benchmarks breakdown

	Benchmark	main	script-update-starter-projects	Change
❌	test_get_and_cache_all_types_dict	857.9 µs	1,095.3 µs	-21.67%
❌	test_setup_llm_caching	1.3 ms	4.1 ms	-67.32%
❌	test_successful_run_with_input_type_text	197.1 ms	250.6 ms	-21.33%