Having been infected with one strain of SARS-CoV-2 doesn't protect you from all other variants. It's not even clear that it protects you from reinfection with the same variant indefinitely.
I was infected with Delta 9 months after one of the initial strains. I was more or less as sick as I was the first time for a full two weeks.
That said, when I looked up studies on that the chances were about 1% for that to happen to me (at that time).