Testing: how to balance coverage, speed and maintainability?

I'm currently designing tests for an application I'm developing, and I'm having problems balancing code coverage, test speed and maintainability of the tests. Let me explain:

I can build a lot of unit tests which will get me 100% code coverage and are quick to run, but they're testing very specific things about very specific functions, so whenever I refactor the code I have to change a bunch of unit tests, which hurts tests maintainability.

Alternatively, I can build a bunch of functional tests that cover every possible path code, but then these tests would be very slow to run (since I would be connecting to real databases, APIs, etc…).

I'm looking for resources, tips or ideas on how to properly build tests such that I don't fall into these issues. Thanks in advance for any help or guidance you can provide me.