How should I explain to my colleagues why to use a object oriented approach or even dependency injection when they write mostly only static methods in our projects?
Points like testing and maintenance don‘t sadly work.

Try to build one class with tests where you can show the benefits and also remember to not try to go all out but start with a few classes where it gives the most benefit.

Once people can see it working its easier to ease into the rest and do not go for code coverage but focus on enforcing correct behavior in some business rule class.

There are an exercise called Guilded Rose where unit tests are a good way to first document existing behavior before rebuilding.

https://github.com/emilybache/...

So they somehow used object oriented procedurally ?