Another thought and a couple of anecdotes:
When you say "there's nothing new" in the house, are you sure there's
absolutely nothing new? No new light bulbs, appliances, public utility changes like them installing remote metering of electricity, water, gas consumption (all of which use cellular connections), alarm system, WiFi infrastructure etc?
Anecdote #1, big: I have a client who owns a recording studio in Halifax, Nova Scotia. Big, professional set-up with a Neve V 48 channel console, Studer tape machine etc. A few years back he reached out to me to say that the noise floor in the console had jumped dramatically over night. After a whole lot of "check this, look at that" back-and-forth I remembered that when I commissioned the console, it really didn't settle down until I connected the central ground point on the desk to the studio technical ground, a copper bus bar in the machine room that was tied to the building (an 1800's vintage warehouse) service entrance ground with #4 or #6 insulated copper wire. I asked the owner to verify the desk connection to the bus bar...all good. Then I suggested that he verify the run to the service entrance (which was three floors below) and, Bingo! There were some trades doing some renovations in the basement, and they had cut the ground wire because it was in their way
. Reconnecting the ground wire fixed the noise issue.
Anecdote #2, small: I had a client who bought an Aurora Audio GTQC Rev Ten from me (that's the channel strip...mic pre, Eq and comp in 1-U), brand new (I'm the Canadian dealer / service rep). After he started using it, he reported a noise issue. This was a few years back and, again, I'm having a hard time characterizing the noise...it was faint, but it was there. He had bought that unit because he had a friend / mentor who already owned one so they exchanged units to see if the fault moved with the unit. The new unit was totally quiet at the friend's studio, and the friend's unit was totally quiet at his studio, and yet still exhibited the noise when he got it back. Well, this was enough to cause me to go and do a house call at his "studio"...the basement of his parent's home. As I was getting set up, I was looking for a convenient outlet to plug in my test set, while we were listening to the noise. There was some little white box plugged into the nearest outlet to his set-up and I asked if I could unplug it to power up my stuff. He said "ok", and the noise stopped as soon as I unplugged it. "It" turned out to be a ****** little WiFi booster that he was using to get better coverage down in his corner of the basement. Now, the reason his friend's unit was quiet when he tried it is that the friend had an earlier version of the GTQC...the Rev ten version has a "Blend" control on the front panel which the earlier version lacked. The Blend control requires an extra amplifier stage and the noise was getting into that amplifier.
So, the moral of both stories is: Sometimes changes happen that you didn't do, and sometimes things that you do not associate with your audio set-up (iow: not part of the signal path) are the source of your audio problems.
Since Paul's latest post came in while I was writing this, a couple of notes:
1) The OP has already stated that unlike the usual noise issues you get with guitars, walking around the room with the guitar does not change the level of the noise.
2) That he has tried multiple guitars, with hum-bucking pick-ups, so that tilts away from loose nut and other hardware issues on the guitar (although I'm a big fan of tightening hardware when noise issues arise so it wouldn't hurt to check that on ALL his guitars).