What's wrong with my rear wheel? Wheel moves about 1/4" front to back when brake is fully applied, cassette seems a bit wobbly, some rubbing noise I first started inspecting my wheel because I noticed when I applied my brake while not riding, I could push my rear end and the wheel would turn forward and back about 1/4"-1/2" each way (but the brake is still locked tight) . I took my wheel off and saw that my DT Swiss center lock was loose, so I bought a Park BB tool and tightened it up, but I still have the problem but less now. I see that the wheel is moving @ the center lock just a bit.

Then as I was messing around with the bike upside down, I noticed that my cassette is wobbling ever so slightly.. Is it possible/probable that this is related? There is also some rubbing noise that is not coming from the brake that is difficult to locate.

Is this likely my axle? Hub? Cassette? Thanks!!
I've seen this issue in the past and the culprit was the axle (not the skewer) in the hub had snapped.

Fortunately, the bike was still rideable to a certain extent, as the QR skewer was holding the two broken sections of axle in place. Note that even when the wheel was removed from the frame, it still wasn't immediately obvious that the axle had snapped, until the skewer was removed from the hub. However the whole wheel was replaced ASAP for safety reasons.

Due to the age of the wheel (15-20 years), it was more economically viable to replace the wheel than to rebuild the old wheel with a new hub.