It's been over 24h so this should be permissible, if not please tell me and I'll combine it with the above post/replace it.
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Obviously this doesn't take into account crew changes after commissioning/refits, but eh, also doesn't include starbase crew (since we don't have it for the Pharos and we don't know how many minor ones like the K-series are around/their crew count) nor the 'planetside' starfleet personnel as we both don't have complete space crew numbers and the optimum ratio for Starfleet will differ from any earth bound navy's shoreside/seaside ratio.
Explorers:
Sagarmatha class (10x): 1,680 crew overall (420 officers, 1,260 enlisted)
Tactical Cruisers:
Excalibur class (12x): 1,632 crew overall (408 officers, 1,224 enlisted)
Saladin class (16x): 2,240 crew overall (752 officers, 1,488 enlisted)
Engineering Cruisers:
Radiant class (4x): 376 crew overall (124 officers, 252 enlisted)
Newton class (30x): 3,330 crew overall (1,110 officers, 2,220 enlisted)
Archer class (22x): 2,816 crew overall (484 officers, 2,332 enlisted)
Cygnus class (22): 1,892 crew overall (484 officers, 1,408 enlisted)
Science Cruisers:
Kea class (12x): 2,376 crew overall (576 officers, 1,800 enlisted)
Frigates:
Selachii class (22x): 1,056 crew overall (264 officers, 792 enlisted)
All in all the non-station spaceside personnel count for Starfleet in 2240 is 17,398 of which 4,622 are officers and 12,776 are enlisted.
All in all, quite a bit less than I was expecting, though the absence of station crew counts (and presumably those of lesser craft that are below our level of abstraction) probably cut the final count down quite a bit.