3.75 mA@6.3V.
Those would be AMPS, not ma = milliamps. Obviously the tranny can power that many tubes, filament-wise.
Are you sure the "6SC6" is not a 6CS6? This is a mixing heptode, used in some transceivers. Bunch of grids, still a low current tube, 2 ma or so.
The 6CS6 is another .3 amp heater. They all run off 6 volts, so, across a transformer running from 120 volts, we would divide their req'd current by 20. So filament wise they would need 3.75 / 20 = .1875 amps powered from 120 volts and use 3.75 * 6.3 = 23.63 watts.
[is there a 6.3 volts pilot lamp typically 150 ma?]
Let's call it 25 watts for the fils.
That leaves 23 watts for your plates, subtracting 25 watts from the nameplate 48 watts.
One figures the 12A_7s use 1-2-3 mils in terms of plate current and same for your 6CS6. So you have 11 tubes using 2 ma each and there you go, 22 mils of plate current required by the whole gang. Very light.
How do we know a garden variety 12AX7 in a preamp uses such low current? Because we go look at a Deluxe Reverb and see an early-stage cathode sitting on top of a 1500 ohm resistor reading 1.3 volts. 1.3 / 1500 = .0008666 amps or .86 ma. 1 mil, basically.
But your question is about "how much can I draw". In my experience, we generally do not encounter power trannies with such large (comparatively) filament capacity with such paltry B+ capacity. This is assuming that the mfr of your device would have much preferred to buy an off-the-shelf transformer instead of having a custom one built. So I would guess that you have some spare B+ capacity. I also assume you are not going to have (as many as) 11 little tubes in your preamp build. Every one you delete eliminates .3 * 6.3 = 1.89 watts of power pulled from the tranny.
Now you have to kind of add all this together. Suppose you wanted to build a SE 6V6 amp in this. You decide to eliminate 4 preamp tubes. So you get back 4 * 1.89 watts of fil power, but your 6V6 will want .6 amp (equivalent to 2 preamp tubes) to light up. Net gain, 2 * 1.89 watts = 3.78 watts. At 250 volts, that's about 15 mils, not really enough for a 6V6. Do we have 15 ma of spare capacity in the tranny? Probably.
If your plan is to build a preamp (only) I can't see there being any problem.