The short answer is that there were no Assyrian texts at the 7th century because the language had been superseded as a literary language by Old Persian, and later much closer to this time period, by Middle Persian. There are no sources written in Assyrian that I know of that speaks to the Arab invasion.

In fact we have no surviving sources of Middle Persian either which comments on the Arab invasion. The only surviving sources that I do know were written in Arabic after the invasions and what is contained within the Byzantine records.