slim4-skeleton VS Fast Route

You can have the container call in a config folder with a file called dependencies or how ever you want. A few existing examples of this is here - Slim calls this app/dependencies in this skeleton project and Odan's Skeleton has this as config/container in their project.

Yes, as an example, the First Application's business logic (not that it's much) doesn't tie itself to the framework, as one example. Odan's Slim Skeleton, ADR Example (yes, I know you are the author), and the Aura Payload example class can be seen as other examples.

Even just the tests in your first link are very useful to see, such as: https://github.com/odan/slim4-skeleton/blob/master/tests/TestCase/Action/Customer/CustomerCreatorActionTest.php

Another option, to me and speaking to the OP as an alternative, it is simpler to add some Data Mappers/Repositories to abstract away the Database code. Good examples is the sample ADR application, Payload library example, Slim 3 First Application, or this Slim 4 Skeleton application

You could also use a Slim Skeleton like Odan's which incorporates much more features to help - docs.

Try Slim again. The setup may be too much, but the concept is the same. Look at the first application or any of the skeleton apps to help (https://github.com/odan/slim4-skeleton for one).

Adding https://github.com/nikic/FastRoute for comparison

Just to show an alternative: https://github.com/nikic/FastRoute

How hard did you look? There are plenty out there. FastRoute, Phroute, based on FastRoute, with basic middleware, League/Route - routing with middleware, using FastRoute, PSR 7 & 15, Slim Framework, at it's core, it like League/Route, etc. None of these require a full framework to use.

I'd recommend looking at the routers for popular, simpler frameworks (both documentation and code) such as Slim. Also look at FastRoute which is the basis for most modern routers.

Using a router library like FastRoute or Phroute to show the example

I've just recently started using https://github.com/nikic/FastRoute and it seems to work pretty well

I think a more popular one like https://github.com/nikic/FastRoute would benefit someone learning more than Aura.

The basics is the RouteCollection - https://github.com/nikic/FastRoute/blob/master/src/RouteCollector.php

Nikita Popov, author of FastRoute wrote a pretty good and complete article about how it works.