First of all, thanks a lot for having a look at it so quickly.

I'm trying to understand this change before merging it.
Could you please explain how this reduces the image size?

And will this guarantee that the SDK permissions are still set correctly for unity versions (different SDK versions / locations)?

See reference above, since we no longer 755 the android folder, the sdk manager is also no longer covered. So should we bring back that line as well?

I'm trying to understand this change before merging it. Could you please explain how this reduces the image size?

So, apparently a big recursive chmod increases image size by a lot. See here for example: ubuntu-2021.2.6f1-android-0.16.0

This change moves the chmod command into the builder image, so a new layer is not created in the resulting editor image.

See reference above, since we no longer 755 the android folder, the sdk manager is also no longer covered. So should we bring back that line as well?

/opt/unity/editors/$version/Editor/Data/PlaybackEngines is a parent directory for all the modules installed by Unity. That includes SDK, NDK and OpenJDK. I did it like this for simplicity.