Can a HDD infect a computer if you only plug it and not boot on it ?

I'm trying to understand if my situation is pure coincidence or not.

I bought a new computer (win11) recently and everything was fine, the whole computer was new. Today, I connected and old HDD on it that I used many years on my old computer, I did not run or read anything from it. It may contains malwares, as when I was younger I probably downloaded random softwares from internet...

Tonight I got a mail from microsoft saying that there have been two suspicious successful authentifications on my microsoft account, one from brazil and the other a bit later in india, both on windows, edge.

What's very strange is that I changed my password only some days ago (i forgot it), so I have no ideas how they managed to connect...

I changed my password instantly and activated double verification, but now I'm worried that my new computer might be infected as well...

Is it possible to get infected like that ? What should I do ?