well that was an interesting experiment. the speaker is A-OK.
That tells you the preamp circuit is Noise Prone,, not uncommon even with big name brands.
preamp out to another amp: white noise and some distortion- but of a different character.
Most likely because something has changed (different circuits and diff speakers)
Your Fender has Excess hi frequency again a common issue with clean channels,, not enough thought in design stage.
They build these things and unlikely they do any R&D
preamp out to mixing board: same result, white noise and occasional static, but not the light distortion tail.
The signal in this case might not be passing through the rather complex switching and that might be where the signal is clipping,, way over my head to guess why.
I steer clear of amps like this that try to do all this fancy switching,,,
IME I often find the Audio is fine it's the switching crap that fails.

stomp box/amp sim into power amp in: near-perfect. If i just wanted a speaker only, all would be well. Going in this way it sounds great, aside from barely noticeable noise.
The sim is likely limiting the bandwidth and hence a much sweeter result because you have bypassed the crappy preamp
The Fender preamp has likely way too much bandwidth and that is evidenced by the harsh brittle sound in your recording.
without a scope it's a guess as to what part of the preamp is causing the problem.
So the speaker definitely is not the problem.
Agreed.

Does this experiment rule out the filter caps?
You have already proved the rectifier and main filter caps are working as they should,,, don't try and fix what ain't broke.

Understand that amps like this are very complex are often a nightmare to resolve.
I've built several dedicated preamp systems for players and bypassed the whole front end of there crappy combo rigs.
The chance of finding let alone fixing the problem is low. All I can say is either sell it or bypass the preamp.

Only other option might be to try the stomp box and Sim into the front end and see if that improves the outcome.
My hunch is the switching chips maybe at the root of this,, along with bandwidth issues.
Others here might have better options for you to try as some here have way more experience that myself.
Phil.