docs: refactor exception usage #4249

Job	Run time
pyright	1m 52s
validate	19s
slotscheck	1m 29s
mypy	2m 8s
Test server integration (uvicorn<0.27.0)	1m 38s
Test server integration (uvicorn>=0.27.0)	1m 32s
Test Minimal Pydantic 1 application	1m 22s
Test Minimal Application with Base Dependencies	1m 20s
test-platform-compat	0s
test (3.10) / test	2m 49s
test (3.11) / test	2m 27s
test (3.12) / test	4m 40s
test (3.8) / test	3m 55s
test (3.9) / test	2m 48s
build-docs	3m 29s
codeql	2m 40s
upload-test-coverage	36s
sonar	59s
	36m 3s

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