Refactor execute_request to reduce redundancy and improve consistency #2021

Job	Run time
build (ubuntu-latest, 3.8)	2m 59s
check_release	1m 59s
build (ubuntu-latest, 3.11)	2m 58s
build (windows-latest, 3.8)	2m 59s
link_check	4m 4s
build (windows-latest, 3.11)	5m 12s
build (macos-latest, 3.8)	6m 46s
Make SDist	31s
build (macos-latest, 3.11)	5m 24s
build (windows-latest, 3.9)	4m 4s
build (ubuntu-latest, pypy-3.8)	3m 18s
test_docs	3m 6s
build (macos-latest, 3.10)	6m 38s
Test Lint	1m 4s
Test Minimum Versions	1m 59s
Test Prereleases	1m 39s
test_without_debugpy (ubuntu-latest, 3.9)	41s
Install from SDist and Test	1m 40s
coverage	0s
tests_check	4s
	57m 5s

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