Does someone get paid two Foreign Language Proficiency Bonuses for both Urdu and Punjabi (or just one bonus)?

You can get bonuses for multiple languages, up to $1000 a month. How much and which languages are put out by the Army annually. I can't tell you what the current languages are and I don't remember where to find the list. But some hunting on HRC should turn it up

ANY SOLDIER, regardless of MOS/Branch, rank or assignment is eligible for FLPB for a language identified as Immediate Investment or Emerging on the 13 November 2019 "Corrected Copy" Army Strategic Language List (ASLL) with a minimum proficiency level of 2/2 or above. Languages identified as Immediate Investment or Emerging are paid at the Payment List "A" rate in accordance with AR 11-6, Table 4-2.
Because both of those languages are on the current ASLL as immediate investment or emerging, and because you got a 3/3 in both, you should get paid $400/mp for each, or $800 total.
Pay starts the day you tested and expires 365 days later.
Your Readiness NCO has to submit that monthly to USPFO.
Since you are not in an MI unit, your Readiness NCO probably won't be versed in how to process FLPP, so have them contact USPFO, and reference AR 11-6 and this:
https://www.hrc.army.mil/content/Foreign%20Language%20Proficiency%20Bonus

Did you check the current Language list? Both are listed individually. You would need to test for both in both reading and listening but you could make it happen.
https://www.hrc.army.mil/content/Foreign%20Language%20Proficiency%20Bonus