Taught by whom? Who but a Forsaken would know those "rare weaves" to teach Elza?

Not Semirhage, she was a prisoner then. There's no evidence another female Forsaken was involved, and it makes little sense to use Elza to free Semirhage if another Forsaken was there and could do it, or to let Semirhage deal with Elza's compulsion if the all-time specialist Graendal was with SH. Mesaana? Unlikely, after what happened in the prologue. The mindtrapped pets? It makes even less sense than the others that SH would not simply have had one of them do the deeds if he had one with him.

There's also the matter of Cadsuane's inverted wards. In the Forsaken know "rare weaves" to unravel them, what's all the fuss they're making about Rand's wards? Demandred and the others have had like forever to loot the vaults in Tear, and take Callandor, and there they don't have Mesaana's motive not to raise the alarm in the Tower unless she needs something really badly.

So, that leaves Shaidar Haran. How likely is it that he can teach rare weaves of saidar? To quote you, the chance of that is zero. But what are the odds he can teach and give permission to tap the True Power? Excellent odds, I would say. "Rarely known weaves" can perfectly be an euphemism for TP weaves, all the more since Brandon also said the whole experience was most unpleasant for Elza. Let her use the TP this once for a special mission for SH is pretty harmless too - she won't be able to tap it anymore without express permission. We also know SH didn't do all this himself and he had to use Elza because, as Brandon explained, he is limited in how he can interact with physical reality. That suggests strongly SH was acting alone in this mission.

Semirhage felt nothing of what Elza did to kill the two women outside. No other woman around did either. All Semirhage noticed was that her shield was gone all of a sudden. No one in the manor felt any of Elza's channelling either. She stole the DM in complete immunity.

There's a whole lot speculative stretching to do to have her learn rare saidar weaves, and while there's no definitive proof she was taught to use the TP, the chance it's precisely what she did are much higher than zero. Over 50% is more like it...