test: Fix for Pydantic private fields (2nd attempt) #4001

Job	Run time
mypy	1m 19s
pyright	1m 1s
Test server integration (uvicorn<0.27.0)	57s
validate	14s
Test server integration (uvicorn>=0.27.0)	55s
slotscheck	33s
Test Minimal Application with Base Dependencies	38s
Test Minimal Pydantic 1 application	41s
test-platform-compat	0s
test (3.11) / test	1m 50s
test (3.12) / test	3m 32s
test (3.10) / test	2m 1s
test (3.8) / test	3m 10s
test (3.9) / test	2m 5s
build-docs	2m 40s
upload-test-coverage	15s
codeql	3m 8s
sonar	59s
	25m 58s

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