What does the process look like for a Prior Service enlisting back into the same MOS?

There are a lot of steps for a Prior Service Soldier enlisting, but based on your statement above, I'll assume away all of those (i.e., you've already been through service verification, checked against business rules in REQUEST, etc.).

Your recruiter should have gone over all of this with you already, but here's the run-down.

You'll be processed through MEPS as normal as there are a lot of things they they will have to verify and administrative tasks completed prior to your enlisting. After all the processing (and assuming to hiccups), then you'll be sent directly to a unit (since you enlisted for the same MOS and have less than a 3-year break in Service).

As you have been discharged over 90 days, you'll receive a full uniform issue (including AGSU).

If you are under six months from when you were discharged (i.e., 180 days or less), then a lot of stuff at MEPS is skipped (medical is the big one, assuming you still meet the standards for medical retention). If 181 days or more, then you'll process though medical as normal, but other items may be skipped (e.g., ASVAB testing)
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* AR 601-210 (Active and Reserve Components Enlistment Program) - https://api.army.mil/e2/c/downloads/344222.pdf
* USAREC Regulation 601-210 (Enlistment & Accessions Processing) - https://recruiting.army.mil/Portals/15/Documents/Forms%20and%20Pubs/Regulations/UR%20601-210_1.pdf
* Joint Regulation (AR 601-270) - Military Entrance Processing Station (MEPS) - https://health.mil/Reference-Center/Policies/2011/09/13/Military-Entrance-Processing-Station

What does your recruiter say?

If you are re-enlisting in the NG, and your exit physical has a PULHES attached then you should be able to utilize that PULHES so long as you complete enlistment within a year of the physical.