The tests serve different purposes. Overlap is good.
The 'overlap' of higher order tests (such as API) and Unit tests should be high. In fact 100% would be good.
Unit tests mock and stub all dependencies. API tests do not. API tests may involve calling many units via the initial call. A unit test should test only one unit. Unit tests are involved in TDD as the code is being written. API tests are often at a higher functional level, part of BDD tests, etc.
The same is true for UI tests btw. One high level test that goes through multiple screens may call several API's which in turn call hundreds of individual units of code, each of which has unit tests. This add to us calling it a pyramid.
Another fun challenge for tests is that as they grow... you need tests for them. The tests that is. For example, finding orphan or duplicate page object identifiers, created as part of testing, is part of testing the tests.
to allow testers access to unit test code so they see what was already been covered by tests. And for the other cases, testers should write new test cases or return the ticket back to the dev until all relevant test cases have been covered.
Indeed tests are documentation. They help communicate both high level functionality (API, integration, UI tests) and low level implementation (unit tests) so they can help both groups. Devs can check the actual functionality being desired (or changed and also not broken). Testers can dig into bugs and edge cases and know why they are happening (and find more). The oft stated independence of the two groups can be handy and indeed a different mindset is very helpful but I've also found more communication is also a good approach. Both (independence and communication) are possible when both groups specialize in the value they add.
As for the 'real world' balance. As usual, that depends. one thousand users or 100 million? 1 developer or 15 ? Budget of $10,000 or budget of $$60,000,000, timespan of this week or next year, criticality of Mars Mission vs automatic birdfeeder program, etc.