Criminals can be on death row for a while. But really everything about Barriss Offee's fall to the dark side, the temple bombing, Ahsoka being framed, and Ahsoka's trial were poorly written and contrived in my opinion.

I think it's because the goal was to eliminate Ahsoka. And if it didn’t work out, then there was no point in executing Barris.

Barriss' confession was only given in evidence at Ahsoka's trial. Barriss would have to have her own trial before being sentenced.

Ahsoka was never sentenced to anything, it was only Tarkin who waved the death penalty card. Even if she were convicted, that doesn't automatically mean that Tarkin's demands would have been met, it's up to the judge. And since Palpatine was the judge, he would have found some way to either pardon Ahsoka or set her free in other ways, death penalty or no (it'd be too risky for Palps to incur Anakin's wrath if he were in any way connected to his apprentice's death).

Really Ahsoka was sentenced to death???

She was facing a death sentence.

It is wierd that she was not killed after, but in original ROTS footage she is order 66d

That would be Shaak Ti, lol. Ahsoka did not exist in that time.

^x5 Maybe Palpatine wanted her out of the way, because it would make Anakin further turn to the dark side

Again, if Palpatine was connected to her death, it would do the opposite. Anakin would not forgive that. To get rid of Ahsoka, Palps would need to do it in a way that would not implicate him directly, a way in which Anakin would not have him to blame.

And think about it, what would make Anakin more trusting and dependent on Palpatine? Him sentencing Anakin's dear apprentice to death, or him being the instrument that exonerates her in face of Jedi indifference and inaction?