To target by precinct in Action Network, go to "Field Values" (it's near where you would add a tag).
Then, search for the field "Precinct 2022."
Enter in the precinct you want to add -- make sure to spell it exactly as it appears in VAN. (You can use the process in Filter a List Based on Precinct to find how precincts are spelled in VAN)
Repeat this process until you have all the precincts you need.
You can save the list of precincts as a Query in Action Network, so that you don't have to add all the precincts every time.