The Non-Chalcedonians seemed to hold that she was Miaphysite, perhaps
@dzheremi could I enlighten us on that.
I could not find her in the Coptic synaxarium which is available in English online (that doesn't necessarily mean anything, as it is incomplete), but here is a bit on her from the Ethiopian synaxarium I have (the one that is translated by Wallace Budge).
With the understanding that I am posting this in response to requests for information and not to start a fight, from the entry on February 21 (Ethiopian calendar: Yekatit 14), we read as part of the entry on Severus of Antioch the following description:
Now he (Severus) only remained in his office for a few days, for the emperor died, and there reigned in his stead another emperor, who was an infidel, and who believed in the Council or Chalcedon, and whose name was Justinian; now the queen, whose name was Theodora, belonged to the True Faith. And the emperor was afraid of this saint, for [he refused] to enter the unclean faith [of Chalcedon], and he would not obey him. And then the emperor was exceedingly wroth with him, and he imagined that the saint was afraid of him, and would submit to him; but the saint would not hearken to his command, and he was not afraid of his wrath. And the emperor wished to kill him secretly, but the righteous Queen Theodora, knowing this, warned the saint to flee from the face of the emperor, and he went forth secretly.
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While I haven't read it myself, Susan Ashbrook Harvey (of
Holy Women of the Syrian Orient fame), has written on the place of Empress Theodora in the Syriac Orthodox tradition in her work
Theodora the "Believing Queen": A Study in Syriac Historiographical Tradition (2011), which is available from Gorgias Press (where else) if you happen to have a spare zillion dollars lying around. I believe that originally appeared in an issue of
Hugoye (Syriac studies journal), though I don't know which one.
So it seems that the Ethiopians and Syriacs venerate her, the Copts maybe not (there are several Theodoras in the synaxarium, but none of them are the empress), and as usual I have no idea about the Armenians.
As you might imagine given our less uniform practices (in comparison to the EO), it wouldn't be unheard of to have a figure venerated as a saint in some churches and not in others.