Add handling to propagate dependencies for submitted flow runs #20179

Job	Run time
docker, python:3.9	4m 55s
docker, python:3.10	4m 50s
Server Tests - python:3.9, postgres:14	5m 31s
Server Tests - python:3.10, postgres:14	5m 26s
docker, python:3.11	4m 43s
typesafety	2m 10s
Server Tests - python:3.11, postgres:14	4m 59s
docker, python:3.12	4m 51s
Server Tests - python:3.12, postgres:14	4m 45s
Server Tests - python:3.9, sqlite	5m 26s
Server Tests - python:3.10, sqlite	5m 22s
Server Tests - python:3.11, sqlite	4m 55s
Server Tests - python:3.12, sqlite	4m 40s
Database and Orchestration Tests - python:3.9, postgres:14	6m 19s
Database and Orchestration Tests - python:3.10, postgres:14	6m 22s
Database and Orchestration Tests - python:3.11, postgres:14	5m 40s
Database and Orchestration Tests - python:3.12, postgres:14	5m 37s
Database and Orchestration Tests - python:3.9, sqlite	7m 9s
Database and Orchestration Tests - python:3.10, sqlite	6m 52s
Database and Orchestration Tests - python:3.11, sqlite	6m 16s
Database and Orchestration Tests - python:3.12, sqlite	6m 1s
Client Tests - python:3.9, postgres:14	9m 16s
Client Tests - python:3.10, postgres:14	9m 14s
Client Tests - python:3.11, postgres:14	8m 18s
Client Tests - python:3.12, postgres:14	8m 26s
Runner, Worker, Settings, Input, and CLI Tests - python:3.9, postgres:14	6m 28s
Runner, Worker, Settings, Input, and CLI Tests - python:3.10, postgres:14	6m 18s
Runner, Worker, Settings, Input, and CLI Tests - python:3.11, postgres:14	5m 40s
Runner, Worker, Settings, Input, and CLI Tests - python:3.12, postgres:14	5m 41s
	2h 52m 10s

Provide feedback