refactor: Clean up lms/envs/production.py cruft #33206

Job	Run time
collect-and-verify	3m 8s
lms-1(py=3.11,dj=pinned,mongo=7.0)	8m 57s
lms-2(py=3.11,dj=pinned,mongo=7.0)	10m 32s
lms-3(py=3.11,dj=pinned,mongo=7.0)	13m 59s
lms-4(py=3.11,dj=pinned,mongo=7.0)	19m 23s
lms-5(py=3.11,dj=pinned,mongo=7.0)	10m 0s
lms-6(py=3.11,dj=pinned,mongo=7.0)	14m 57s
openedx-1-with-lms(py=3.11,dj=pinned,mongo=7.0)	10m 2s
openedx-2-with-lms(py=3.11,dj=pinned,mongo=7.0)	13m 17s
openedx-1-with-cms(py=3.11,dj=pinned,mongo=7.0)	7m 19s
openedx-2-with-cms(py=3.11,dj=pinned,mongo=7.0)	6m 21s
cms-1(py=3.11,dj=pinned,mongo=7.0)	3m 25s
cms-2(py=3.11,dj=pinned,mongo=7.0)	12m 6s
common-with-lms(py=3.11,dj=pinned,mongo=7.0)	8m 7s
common-with-cms(py=3.11,dj=pinned,mongo=7.0)	4m 6s
xmodule-with-lms(py=3.11,dj=pinned,mongo=7.0)	7m 20s
xmodule-with-cms(py=3.11,dj=pinned,mongo=7.0)	7m 41s
xmodule-with-cms(py=3.11,dj=pinned,mongo=7.0)	7m 19s
xmodule-with-lms(py=3.11,dj=pinned,mongo=7.0)	7m 26s
Unit tests successful	4s
compile-warnings-report	12s
coverage (3.11)	1m 31s
merge-artifacts	6s
	2h 57m 18s

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