If, after confirming the impeachment, the Senate voted to bar Trump that would of course stop him running for president in 2024. But that's not the only way.

There's a strong case for arguing that he's already barred from doing that under the 14th Amendment. Whether that applies would need to be determined, ultimately in the Supreme Court. That could come through a case against him for his role leading up to January 6th and on that day.   If there was no such proceeding it would be likely to arise any time he starts to campaign for President.

Even if theSenate fails to muster enough votes against him to convict, that would in no way amount to an acquittal of the criminal charge of supporting insurrection.