[Attempt 2] refactor: Clean up lms/envs/production.py cruft #33256

Job	Run time
collect-and-verify	3m 12s
lms-1(py=3.11,dj=pinned,mongo=7.0)	12m 54s
lms-2(py=3.11,dj=pinned,mongo=7.0)	10m 50s
lms-3(py=3.11,dj=pinned,mongo=7.0)	14m 13s
lms-4(py=3.11,dj=pinned,mongo=7.0)	20m 1s
lms-5(py=3.11,dj=pinned,mongo=7.0)	9m 40s
lms-6(py=3.11,dj=pinned,mongo=7.0)	15m 9s
openedx-1-with-lms(py=3.11,dj=pinned,mongo=7.0)	9m 50s
openedx-2-with-lms(py=3.11,dj=pinned,mongo=7.0)	14m 15s
openedx-1-with-cms(py=3.11,dj=pinned,mongo=7.0)	13m 46s
openedx-2-with-cms(py=3.11,dj=pinned,mongo=7.0)	5m 44s
cms-1(py=3.11,dj=pinned,mongo=7.0)	3m 37s
cms-2(py=3.11,dj=pinned,mongo=7.0)	11m 12s
common-with-lms(py=3.11,dj=pinned,mongo=7.0)	8m 53s
common-with-cms(py=3.11,dj=pinned,mongo=7.0)	5m 46s
xmodule-with-lms(py=3.11,dj=pinned,mongo=7.0)	7m 33s
xmodule-with-cms(py=3.11,dj=pinned,mongo=7.0)	11m 47s
xmodule-with-cms(py=3.11,dj=pinned,mongo=7.0)	8m 6s
xmodule-with-lms(py=3.11,dj=pinned,mongo=7.0)	7m 54s
compile-warnings-report	11s
Unit tests successful	4s
coverage (3.11)	1m 39s
merge-artifacts	10s
	3h 16m 26s

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