Smoke on my power amp

the first question is "why?".  I have a guess: yo disconnected the speaker wires and they touched, shorting out the amp's "unconnected" channel.  Guess.
IS there permanent damage?  Maybe. Some, yes. Significant? we don;t know without looking. Could be nothing more than heat from an emitter resistor that began cooking. Its not good for it, but it might more or less survive. BTDT in the lab.
But the bottom line is you did something more than you think you did; and the fact that you have to ask, says "take it to someone who can check it out thoroughly".
G

All I know is that the vast majority of amps I own or have owned have a huge warning in the owner’s manual that states not to operate the amp without speakers being hooked up. And I think you now know why. It is NOT safe to operate so don’t even think about it...

I thought I’d weigh in here. Basically this means the vast majority of your amps are fundamentally unstable. An open circuit is the easiest load on the planet - no current flows -- on the condition that the amp is stable. Inherently stable, not "stable when driving loads we kinda hope are there". It usually means that am amp is not inherently stable, **and** that the speaker load forms part of the feedback loop. Note this is a problem with opamps, and is corrected by either "compensating" it (which has side effects) or operating it only within certain parameters - typically not unity gain. Ive designed dozens of amps of various types (chip based, BJT, FET, valve/tube...), some for myself, some for production, some for others to produce, or derive something from. Every single one was unilaterally stable. Open circuit? Might as well be off. Happy as a clam.
So the above may well be true, but in my opinion its a sad situation. I think I’ll go upstairs, unplug the speakers and turn the volume to 11. Just because I can.
So, in the end read the owners manual. but also wonder why the condition is so. To be totally fair, my stuff has some odd requirements too (so read my manuals!) - mostly because i typically leave certain low-power-draw parts operating 24/7 for a variety of sonic reasons - and without on/off cycles they last longer, not shorter. Odd but true.  I used to tape the fuse to the part of the owners manual with warnings. People woudl call up and say "it wont turn on". Did you read the manual?  Humm? Notice anything?  :-)  G

in the specific case of tube amps having output transformers

Fair enough!  (But we were talking SS...)  Also that is more an issue of disconnecting while playing, rather than "turn on with no load" - which are quite different.