Yes, make sure that the MB you are ordering is the exact same one as you have now. You have the Part Number. Make sure there isn't any sort of revision. There have been times where a manufacturing does an update to a part and keeps the same Part Number but notes a revision similar to how desktop motherboards are.
In this case, since everything is integrated, you have to make sure it all matches. The part should include the GPU and CPU with the Motherboard.
As noted by
@eidairaman1, mobiles now are one and done. They are not designed and meant to be flashed or cross-flashed. There are different versions of the mobile GPUs now and it isn't standardized since MXM modules pretty much went away. The manufacturer can set the power limits, clock speeds, etc. to suit how they want that particular system to run.
As noted in the TPU database. Each of the below would have their own SKU/Part Number attached to them.
GeForce RTX 3060 Mobile 80W = 900-1425 MHz
GeForce RTX 3060 Mobile 85W = 1035-1485 MHz
GeForce RTX 3060 Mobile 90W = 1163-1530 MHz
GeForce RTX 3060 Mobile 95W = 1215-1567 MHz
GeForce RTX 3060 Mobile 100W = 1267-1605 MHz
GeForce RTX 3060 Mobile 105W = 1305-1642 MHz
GeForce RTX 3060 Mobile 110W = 1342-1680 MHz
GeForce RTX 3060 Mobile 115W = 1387-1702 MHz
For the issue you are having now, I would order a replacement, install that into the laptop and get it up and running.