Getting OEM parts from a local dealership, how long is the wait (typically.)

It really depends on where you live. The closer to a large metropolitan area the faster the parts will arrive.

As others have said…Why dealer parts. You can get aftermarket parts that are as good or better. And a large portion of parts on you vehicle are NOT made by the manufacturer…but instead made by different parts suppliers who also sell those exact same parts to places like NAPA or OReily’s.