I think one detail people are suggesting is that somehow the sending stud on the tank unit is grounding out when installed
Like maybe it has a manufacturing defect or some how part of it on the underside is contacting the tank or something
The idea being that it is the most likely area you should focus on now

Ohm out the sending unit sending wire stud to the sending unit body (ground) with it outside of the tank
And move the float arm up and down to confirm it works properly
Then with the meter connected up to the sending unit sending wire post place but dont screw the sender into the tank and repeat the measurement while giggling the unit

At this point the ohm meter should be reading about 20-25 ohms perhaps with 3/4 full of fuel
If you see that ohm meter drop to 0 ohms intermittently at this point you will have confirmed the sending unit is somehow shorting out when it’s being placed into the tank hole

The next step would be to carefully examine the sending unit bottom and top side and try to figure out where its shorting

Can you post a photo of all sides of the sending unit?
There is more than one style and that might help us help you
-s