Massive, Sudden fish loss-Seeking advice

I had a nice stable 10 gallon tank with 10 fish- 5 tetras, a couple
barbs, zebra danios. The fish had live several years and the tank
looked good with regular siphoning of the bottom and water changes.

The trouble started when I bought a new tank. I started it up and a
week later bought some fish. To introduce them slowly into the new
tank, I put a few into the old tank for a couple of days.

A couple of days later, all 5 neon tetras died overnight. over the next
couple of days, the rest of my fish died. Same thing in the new tank
which was mostly guppies.

Before the hardier ones died, they swam frantically, and often swam
upside down or vertically. When dead they sank to the bottom instead
of floating on the surface. Some of the dying were covered in white
"fuzz", but not all.

I check the pH and Nitrates, Nitrites and they were fine

Two questions: 1) Anyone know what might have caused this?
2) Any advice on how to clean the tank/ what to do before introducing
new fish?
Thanks