My project depends on over 150 external packages. We just do integration testing or manual testing. Update your dependency, check the feature that depends on it.

You need to describe the problem more. I do not check all deps are compatible with each other (in the general language sense, dev tooling is more challenging)

1. Good testing and CI

2. Run updates, see if they work, adjust deps as needed (very rare)

tl;dr I don't have your problem, I know some things about dep mgmt systems, have scars from rolling updates org wide, but not enough about your situation to offer pointed advice.

When I cared about this the answer was always test automation. If you can test almost everything in 30 seconds you can multiply that against each version of your application and be done in a few minutes.