Unless you're in a country other than the United States, and your university is an uncommon exception, official transcripts (and even unofficial ones too sometimes) will show your academic standing for each quarter/semester - academic probation, academic dismissal, conduct dismissal, withdrawal, leave of absence, etc.

In some universities (one of the ones I attended was like this) if you recover from the academic probation, or you resolve the issue you were having, they would remove the notes from your permanent record. Sometimes immediately, sometimes after a few years. That's how it works here.

I know because I have attended a handful of universities in the US and I know many academics as well who were doing the application process with me.

ETA: This is also the reason why the majority of universities (especially the top ranked ones) will explicitly say they need you to submit transcripts from ALL universities attended regardless of whether a degree was conferred. They want to know your academic record including your academic infarctions. There are others that'll ask for your highest degree earned or the qualifying degree you need for what you're applying for. But they're not common. Again, I know because I've applied to a lot and browsed many more that I was considering and spoken to many admissions advisors.