Already happening
The state senate (which the Republicans managed to hold) is already making noises about stripping the Lt Gov of many of the powers and prerogatives that are based on senate rules and not codified by statute or in the state constitution. These include committee assignments, choosing legislation to advance or not, etc.
And some state legislators are calling on Greg Abbott to convene a special session so they can limit the power of the Governor’s office as well, before Gina Hinojosa takes office.