Project services should have "recent deliveries", like webhooks

Description

The "project services" integrations should have a "recent deliveries" UI, like custom webhooks. These are extremely useful, if not outright required, to be able to debug what's happening in these external integrations. See my other issue, #3874 (closed), for an example.

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Proposal

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Documentation blurb

Overview

What is it? Why should someone use this feature? What is the underlying (business) problem? How do you use this feature?

Use cases

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Feature checklist

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