How do you investigate a metric change when the evidence is split across tools?

Curious how other teams handle this we're launching in a few days, but wanted to ask here first.

When something important moves (activation, conversion, churn), the evidence is rarely in one place. Some is in product analytics, some in billing, some in error tracking. None of those tools talk to each other.

Do you have an actual process for this, or is it mostly tabs and timestamps by hand? Curious what's worked.