Is my salah valid, or should I consider repeating it?

Assalamualaikum. I'd like to start off by saying that when it comes to praying and wudhu, I always have doubts or am forgetful of whether I did an action or not

During the sujud of the first rakaat, I suddenly doubted whether I did the opening takbeer or not. I could not remember at that point.

However, I reasoned that I probably did as I usually never forget it, and if I did, I always realised it immediately.

I did two prostrations of forgetfulness and everything.

Nonetheless, I'm still worried if my prayer was valid. Since, I heard that if you doubt a pillar, it's like you have not done it. But I'm not sure what to do as doubts like these always come to me in salah.

Should I repeat it?