SB24 can probably answer this the best but I'll try. Shahs and Panchayat do not coexist in real life but they do in Hindi serials.
In the Waaris universe, the Shah is the head of a certain clan. They handle disputes within their own clan (Preet mentioned some of the things she did as Shah in that episode where the villagers tried to punish Amba) and whatnot but they don't rule over the whole village, only their own clan. The reason the issue in the first post leap episode went to the Panchayat is because it was an interclan dispute rather than an intraclan one; the Bajwas were involved as well. The ultimate decision was meant to be up to the Panchayat but they let Manu handle it because they agreed with her solution.
The Panchayat, on the other hand, are elected councils which are primarily found in villages. They do what all councils do, I guess.