I should add that around this time I was trying to use a vacuum cleaner plugged into the GFCI outlet. As best I remember, I tried to turn on the vacuum cleaner but it wouldn't start, and that was when I discovered the outlet had tripped. I reset it, the vacuum came on, and then (I think) I turned on the lights (on a dimmer switch behind the same panel) and discovered the blown bulbs.

I don't think the bulbs flashed before going out. I think they just seemed dead, all three simultaneously.

I'd try one of the "burned out" bulbs on the working side just to
verify they're actually defective.

I tested all three and all three are dead. And I tested one of the good ones in the right side and it worked there.

As it turns out, the vacuum cleaner is a red herring. My wife saw the dead lights the night before but didn't mention it. Still don't know if trying to turn on the vacuum is what tripped the GFCI or if something else did. Or if that's even related.

Condensation from a hot shower can cause the GFCI to trip. It probably wasn't the vacuum unless there was water involved.
If the lights work with the GFCI tripped (push the GFCI TEST button) then they aren't related. I doubt they are if the left side worked when it was tripped.
If the light fixture received a sharp blow when turned on, that could cause bulb failures.

I hope this save you a few bucks.

Here is a link that might be useful: LightBulbEmporium.com

Good point about the lights working while the GFCI was tripped. Yes, they must not be connected, because the left side works just fine while it's in test mode.

I guess that brings us back to what could possibly make three bulbs blow simultaneously. Just freak chance? A weird surge? It's bizarre.

But thank you for the link, saltcedar. Those are about a 1/3 of the price I was seeing elsewhere, so that at least is a relief.

Makes me think this is just pure coincidence. Also, while it can happen, it is also rare for a GFCI receptacle to trip on condensation alone.
I would suspect the receptacle is faulty, depending on the year the house was built, and needing to be replaced. New GFCIs manufactured now are less susceptible to trip.

Now a follow-up question: in sifting through the different sorts I somehow ended up ordering halogen instead of xenon. the halogens work in the fixture, although the fixture says it's not intended for halogen use. Is there really much danger, though? I know halogens burn a little hotter, but it's a relatively open fixture.

Halogen is krypton or xenon gas.
The only difference I know of is the color temperature.
So if they can tolerate Halogen temps they should work
with both gases.

Here is a link that might be useful: Halogen lamps with krypton or xenon