A self-bias amp is hard to hurt the tubes.
> designed to do virtually the same thing as a proper output transformer
Similar idea.
A power transformer must work good at 50/60Hz and (for rectification) several harmonics. It has a steady power input and heat may be a problem.
An audio power transformer works down to similar frequency and up to much higher frequency.
With many simple winding techniques, the power transformer is likely to be "flat" to the top of the audio band, >5KHz. With other winding techniques (especially dual-winding) it may fall badly above 500Hz.
The real limit is voltage divided by frequency. If you go past this, there's trouble. A power winding may be good for, say, 100V at 50Hz. This will also be good for 200V at 100Hz, perhaps 400V at 200Hz (though insulation breakdown may limit re-rating this way).
If you apply too high voltage at too low frequency, the core saturates. Distortion gets very high. Inductance almost vanishes.
In power transformers, distortion is a minor thing. The very low impedance of an Electric Company sucks-up the distortion. A few small transformers on a power line cause no real trouble. (The big transformers on the street are not worked too close to saturation; other factors tend to tune-out the distorted waveform.)
In audio from expensive (for the Watt) high-impedance tubes, distortion is a big deal. A "100V 50Hz" winding probably should not be worked over 30V-40V on 50hz audio or the deep bass will be colored with harmonics. (Which is not necessarily bad for small bass amps which can't really pump 50Hz air: put some hair on it and the ear will re-create 50Hz from the overtones.)
OTOH, audio is not steady 230V, but more soft than loud. Frequently the heat in an audio transformer is totally insignificant.
A more significant hassle is Turns Ratio. Tubes will "work" mis-loaded but Watts output will be down. A 6V6 biased 300V 40mA will do well with a 7K load. Put the 2K OT from a 110V radio on it, power is less than half. (Which is not an amazing change of loudness.) Use a 400r OT from a transistor radio, power output will be way down.
> 120v or 277v primary and a 24v secondary
120:24 is 5:1 voltage and 25:1 impedance. 8r load reflects as 200r, which is much too low to be happy with the usual audio tubes.
Are you USA? 277:24 is 15:1 voltage and 133:1 impedance. 8r load reflects as 1,066r. This superficially looks excellent for a 25L6/6Y6 at 110V and 100mA. At 110V the peak plate swing is say 80V so the RMS is 50-60V, 1/5th of the 60Hz rating, so THD may be low. As could be expected, since I think this may be a 40VA core and you would only be asking 2Watts of audio through it. In SE, the DC in the core puts it at a disadvantage, but 20:1 over-size covers that well.
SE and self-bias amps tend to not go crazy with bad loads. They idle at all the power they can stand. They divert some of that to a load for output. If the load is bad, they are in no worse shape than just idling. Big push-pull fix-bias amps CAN get in trouble, because they will suck more current to cover the load, and if bad, they can bust a gut trying. Less of an issue because few handy power transformers are remotely suitable for the very high voltage primary needed. A 600V 100W 6550 amp has 800V AC across the primary at full roar, and we would expect a 2400V AC rating to keep THD low. They don't let me play with 2.4KV transformers.