PYTHON-5538 Clean up uv lock file handling (#2522) #8135

Job	Run time
static	3m 20s
CPython pypy-3.10-ubuntu-latest	12m 47s
CPython 3.13t-ubuntu-latest	11m 48s
DocTest	1m 9s
CPython 3.9-ubuntu-latest	11m 30s
Link Check	5m 36s
Typing Tests (3.9)	1m 3s
Test async's minimum dependencies and Python	45s
Docs Checks	41s
Make an sdist	17s
Test using minimum dependencies and supported Python	35s
Typing Tests (3.11)	59s
Install from SDist and Test	53s
	51m 23s

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