Does anyone know, is it possible to scan a package and get a receipt and then go back to your car with both? I've "Googled it" and came up zero...

Only receipt is from the teller after you stand in line.

From USPS Website:

"Self-service kiosks provide customers a convenient alternative to the full-service counter."

I buy $196.00 worth of LDs from an LDDb shop and for almost 1 month, tracking says "package is in possession of the USPS". The kiosks accept packages up 15 inches in size. PO is located in Anchorage, Alaska. The question is, when you put the package in, is that when you get a receipt???

I don't have one in the town I live in now, when I did see them I never used them.

You really need to be contacting your seller to try and figure out the problem don't worry about if you get a receipt from the kiosk.

There are times when the people who get the packages at the post office don't scan the package and it sits in limbo until it gets to the next post office.
Media mail can take over 1 moth in certain situations.

I don't use the kiosk nor do I have one nearby but I have received packages regularly from people that use them. Generally there is a small delay between when the person tells me it was dropped off and the scans start. Around a day typically so this is definitely abnormal.

It's also possible that the package is moving and simply not scanning but a month is a long time to be moving through the USPS system.

There must be a reason why most people don’t ship to Hawaii and Alaska.

Well, I just checked the tracking number, and the package has departed the Seattle mail center. Only took 3 1/2 weeks...

Well that's not bad, I got a package 9 or 10 months later from Canada and this was almost 20 years ago.
Media can take up to 6 weeks I believe, but since they are now always short handed it could take longer.