RD shifting troubleshooting is actually some of the easiest troubleshooting that can be done.

From your description I would have started with cables and housings. Make sure all of the pass through points are clean. It sounds like something is hanging up.

Make sure the derail is clean and nothing is causing it to stick. Use your hands to push it through the full sweep without any cable attached. (wheel out of frame as well).

Check the derail hanger. Loose? Straight? Use a DAG tool from Park to check it.

Check the wheel. Any movement in the axle with the wheel mounted in the frame (cone/bearing/locknut adjustment).

Check the cassette. There may not be play in the first few cogs but you may find movement from the middle cogs back. Comes from not getting the lockring seating properly/ having the first cog off.

All that checks out then pull the cable out of the shifter and route it like normal and shift it all by hand pulling on the cable. If it's all free and working correctly then you have a sticky shifter. If that's the case pull the shield on it and spray it with rubbing alcohol and blow it out with compressed air.

Done.