I'm more worried about SMQ. If those secret plans fail, 100% our FM is going to get the blame: "it's because he failed to give a birthday gift to Erdogan's soon to be grandson (yes, we know, good news in 3 months)."
In terms of how the PN defines "large surface vessels..." The CNS said the PN relies on around 10 such ships, which means he's referring to 2,000+ ton ships.
Basically, the F-22P, OPV 1900 (Yarmouk-class), MILGEM, Type 054A/P, PNS Alamgir, etc are all 'large' vessels. Not including PNS Alamgir, the PN has 14 such ships in the pipeline or in service (F-22P), which leaves the 6 larger ships "to be contracted soon."
If the PN is simply looking for more sea control capability, then they could be looking at larger OPVs based on the Damen OPV 1800.
However, if these are to be a fully capable design, then I'd wager it is the Jinnah-class frigate. Since J-Class is a separate program from the MILGEM corvettes, it would be a reasonable bet to expect a large (5,000+ ton) design. The PN is clearly now calling 2,000-3,000-ton ships "corvettes" (i.e., OPV 1900 and MILGEM), so a "frigate" in the Type 054A/P's range (4,000-5,000-ton) is plausible.
Finally, 20 large surface vessels is huge. This would give Pakistan a large navy. For reference, the Royal Navy of the UK is around 25-30 'large' ships (2,000+ ton not including carriers, tankers, etc), and they have global reach. The French have around 24 such ships.