fix(control) Move integration reads to replicas (#122794)

Move a bunch of integration reads to replicas. I've focused on paths
where we're handling webhooks, or using integrations in tasks as these
flows are far away from any writes and I don't want to introduce
replicas in places where we could be exposed to read-after-write. For
this reason, I've also tried to avoid paths where the read integration
is used to construct a client.