I agree with the cloaking concept above as well. I have a book, not yet released on that. Seems to me, PAGs would have also been equipped with cloaking tech since the tech was available at the time and it lends to the successful completion of their duty. Like speed trap cops, unmarked prowlers and undercover officers. Sitting or cruising quietly and stealthily would be Paramount to their ability to conduct successful policing. Plus. Cloaking would be about the only way they could conduct little ship, big ship policing encounters. The ability to vanishing and reapear on the bow of the larger ship at will would be great leverage.
Timo... Torps and supplies would be aquired on a regular, albeit as necessary basis from Starbases under Federation aquaintence or command. Aquisition of such armaments and or supplies would be paid for by the Federation, aquisition division. The Captain or FO would simply sign off for them. Nearly all encounters would result in the use of some or all arms since the PAGs wouldn't be sent unless the locals couldn't handle the issue themselves. Storage for arms wouldn't be an issue. The ships are large enough to store a good supply as well as provide supply storage and crew quarters. Frequent, Star Base stops would provide distractions from combat duties as well.
If I recall the PAG ships were assigned to Starbases and only did local border patrols and hot spot patrols. Their gig was that they were very, very fast in warp and could get to places to interdict ships with heavy firepower for long enough for proper starships to arrive. If the PAG ships survived the encounter, it would go back to Starbase for repairs and resupply. They were never far from any base. In naval terms they're essentially heavily armed Coast Guard ships mixed with hydrofoil designs for rapid response.
I would think that weapons and suppies would be handled through starfleet, the only thing the federation would typically do is dish up money at the beginning of a fiscal year. It doesn't make much sense that starfleet would have to go to the federation every time they needed a box of drill bits.
Similar to Pegasus-class USN hydrofoil PB of the late 70s to early 90s https://en.wikipedia.org/wiki/Pegasus-class_hydrofoil - roughly the size of a patrol vessel, but limited anti-ship missiles (2 Harpooon missile quads for a total of 8 missiles) in addition to the usual defensive/disabling cannon (3") - then?
It's normal speed was poor to moderate, but it's foilborne speed of 48 knots is pretty decent for the era. They were about a third faster than contemporary Spruance-class derstroyers, maybe double that faster than the OHP-class frigates, and about three times faster than the Eagle-class patrol boats they would have replaced (they were actually scrapped before a direct replacement was available, the 90s built Cyclone-class PBs eventually took on the role, which were faster than the Eagles but till only about as fast as the Spruances) and even modern USCG equivalents - the Sentinel-class Fast Response Cutter (28kn) and the Island-class patrol boat (29.5kn) - are considerably slower at max speed. Admittedly on paper they have relatively poor thermal efficiency, but given that they're still used even on modern major warships like the Burkes so they seem to be "about the best of a bad lot" at worst?
The PAG ships all seemed to be pushing Warp Factor 20 (old scale....these are TOS/TMP era ships...the book for them is in the timeline just before Praxis explodes) for relatively short distances. Not sure about their impulse maneuvering, though with the cut down hulls they would have less mass to shove around with the impulse units. Most, if I recall, had cruiser sized phaser banks (but less of them( and one or two photon torpedoes tubes with a limited number of torpedoes.
That seems improbably fast to me, even if we were to use an aviation rather than nautical model, RW applications suggest that maybe four times faster might be possible v. cruisers (SR-71 v C-5), which gives a value of between Warp 12.7 and Warp 14.4 (slightly greater than the structural limit of the Connie of Warp 14.1)
If I recall, the Warp 21 pushing was something like an emergency battle speed that they could burst for maybe ten minutes, while their flank speeds were more like warp 11 and Emergency speeds of warp 14 or 15. Cruising speed was still around warp 8. (how there can be emergency and burst speeds faster than Flank speed....don't ask, not sure) The battle burst was suppose to be for overtaking Orion pirates and Klingon raiders, which should be possible if you are going 8 times faster than they are at warp factor 10 by bursting at warp factor 20. This design was from about 40 years after the Constitution-class was originally being built, using newer technologies. This class is almost a post-Excelsior hull. Its transitional in that they start coming out after USS Excelsior is launched, but before she is in full commissioned service under Captain Sulu. She has bleeding edge cut down versions of the nacelles of the refit era Constitutions. (TNG scale, Warp Factor 20 and 21 are between Warp 9.99 and Warp 9.995. So not quite twice USS Voyager's stop end 'cruising' speed of warp 9.975, but close. It should be noted that in the old DC comics, the USS Excelsior could go at Warp Factor 20.)
I suspect a misunderstanding of the term "flank speed" which should in fact basically be the same or slightly less than the emergency burst/battle speed. The fact that Warp 20 is also faster than fast ships a century later (in objective speed, travel time does appear to depend on "environmental factors" and the completeness of navigation charts etc), still seems a bit off to me could see a flank speed in the Warp 11.5 to 12 range (similar to the "maximum warp" of the Galaxys a century later), but more than that seems a stretch for more than minutes (up to Warp 14 might be doable for that).
Caseless torpedoes can be produced quickly for rapid fire but lack guidance or propulion. They use the momentum given them at launch. They are nothing more than antimatter and matter suspended in a briefly active “magno photon forcefield”. Whatever that is. Cased torpedoes are spheres like the charge taken to the planet surface in “Obsession”. They have guidance and sublight thrust. The Chiclet from TWoK is a warp version of the sublight casing. As for a PA group going out and looking for trouble, as the book describes, there is much more “laying in wait” going on. A lot of work is done to assess threats and predict likely attack routes. The PAs are constantly shuffling along the frontier as the threat scenario changes. In the process, they are involved in clandestine operations as well as diplomacy, so yes, they do look for some trouble. But they are really about being near the right place at the right time and providing a delaying action until reinforcements can be brought up from deeper within the Federation