Add desi_update_processing_table_statuses and update dry_run_level's #5681

Job	Run time
Doc test (ubuntu-latest, 3.9)	45s
Test coverage (ubuntu-latest, 3.10, <6, <2, <1.23)	7m 54s
Test minimal env (ubuntu-latest, 3.10)	53s
API doc completeness test (ubuntu-latest, 3.9)	21s
Style check (ubuntu-latest, 3.9)	21s
Unit tests (ubuntu-latest, 3.9, ==5.0, ==1.1.6, <1.23)	6m 4s
Unit tests (ubuntu-latest, 3.9, ==5.0, <2, <1.23)	5m 49s
Unit tests (ubuntu-latest, 3.9, <6, ==1.1.6, <1.23)	6m 2s
Unit tests (ubuntu-latest, 3.9, <6, <2, <1.23)	5m 44s
Unit tests (ubuntu-latest, 3.10, ==5.0, ==1.1.6, <1.23)	5m 56s
Unit tests (ubuntu-latest, 3.10, ==5.0, <2, <1.23)	5m 48s
Unit tests (ubuntu-latest, 3.10, <6, ==1.1.6, <1.23)	5m 51s
Unit tests (ubuntu-latest, 3.10, <6, <2, <1.23)	5m 36s
	57m 4s

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