I resolved my issues. I guess it's not really the way to go by following the older instruction to build the project.
- Checking the source code out and running `make code/compile` like the CI does is simply enough
- No need to run `make setup` except for `make setup/operator-sdk`. Otherwise, go mod tidy will try to fix the go.mod file, resulting in changes of the file and eventually of the vendor/ folder.
- I refrained from running `make code/gen`. It seems like something has changed in the used generator. Also, as long as there are no changes to the CRD, I think there is no need to run that target.
- You can run this project on Windows, but you have to check the source code of operator-sdk out and build it yourself.
- Regarding Prometheus dependency being readded and double declarations of `log`: This was a mistake on my end; I just messed something up while coding. :)