How much better are newer Panasonic bodies without AA filter for windeangle lenses?

Your G7, if it is a used unit, might have some mount/sensor relative tilt. This sort of thing shows up more clearly with wide angles.

You can do comparisons against the Olympus by focusing on centre, corner, etc.

The four-corners test and infinity horizon test (kenw used to describe them quite well with example images) are good ways.

The infinity horizon test: Find a horizon with say trees or a fence that is sufficiently far away (infinity across the horizon, usually a football field is plenty large enough for a wide angle lens) with details across the entire horizon. Set up the camera so that the horizon is diagonal between two opposite corners going through the centre. Shoot focused at the centre and both corners. Set up the camera with the horizon going through the other two corners and repeat.

Compare across both cameras. You should be able to deduce whether it is a general lack of sharpness in all corners or some kind of tilt, i.e. the lens mount not parallel with the sensor. Typically, tilt will cause corner 3 to be unsharp when focused at corner 1, and vice versa. If this happens with one camera and not the other ...

The four corners test: Find something with detail far away - road sign with different sized lettering is a good candidate. Focus on the sign at the centre. Keep focus unchanged and shoot with that object in the centre and in every corner via re-framing. Then focus on the object with it in one of the corners and repeat the five shots. Compare across both cameras.

The key thing about these two tests is that the tester does not need to worry about keeping the sensor parallel with the target, such as in the case of a brick wall test. This is because for the horizon test, everything is at close enough to infinity that even large non-parallelism does not matter - you don't care, for a wide angle lens, whether one side of the horizon is 70 metres and the other 100 metres away. 70 and 100 metres are essentially the same distance. And the four corners test is on a small target filling less than 1/10 of the image height and there is nothing to keep parallel to anything else in the test at all.

Pure electronic shutters and raw for all tests. A tripod would make things easy.