When it comes to what insurance does or doesn't cover, the best answer will come from the text of the policy itself. This is, unfortunately, very dry reading and most people -- although instructed to keep a copy handy -- don't have the full text nearby. That said, because of the regulated nature of insurance in the USA, standardized forms of policies exist, and homeowner policies are no exception.
The common homeowner policies are numbered HO-1 to HO-8. HO-1 only pays out only for the ten listened "perils", and is thus the most barren policy available. Not all HO-1 policies are verbatim identical, but the gist usually matches.
We can look at this sample text from a random HO-1 (issued by American Family Insurance). Page 5 shows that "fire or lightning" is covered, so that's a good start.
On page 6, we find the exceptions to the coverage, so if any of these apply, the policy will not pay out. Nothing in Part A would seem to apply to a DIY LED project, unless you tell me your LEDs are radioactive. Part B also doesn't apply, unless you're somehow perpetuating a fraud using LEDs.
Part C reads like it could apply, because it mentions "construction", "design, workmanship or specification", and "maintenance", but this section only applies to the dwelling and so refers to those things which are permanently affixed to the house. That would include things like ceiling fans and light fixtures, but wouldn't include stuff that is attached to the walls using thumbtacks or 3M Command strips. It even says that:
However, we do cover any resulting loss to property described in Coverage A - Dwelling and Dwelling Extension not excluded or excepted in this policy.
This clause basically means the exceptions on Page 6 should be interpreted narrowly, not broadly.
The point is, in the entire policy, there isn't a clause that requires listed equipment, and remember that this is the most bare bones policy commonly available. If such a requirement did exist, then building your own PC wouldn't be possible, since the standards bodies do not test individual computer parts -- except the PSU, because that plugs into the mains.
If a fire that damages the house does occur, the most probable causes would be due to: 1) an unlisted power supply or power brick feeding the ESP32 or the LEDs, or 2) no current limiting (eg a fuse) to cut out the power supply. Other failures like a shorted LED are unlikely to actually cause a house fire, and the insurance companies and UL know this; they're more focused on preventing arc-faults that contribute to an estimated 50% of electrical house fires every year.
Good design and clean installation on your part, and using properly listed low-voltage power supplies, will mitigate the major fire risks, leaving just software bugs and lighting snafus for you to deal with.
As a matter of completeness, if there is an unlikely fire, be it from an LED project or from a candle falling over, the insurance company will still pay. But big or small, the claim will be recorded in the CLUE database along with the payout amount. This often reflects negatively on homeowners, so future rate increases may occur. But that varies by state. In any case, though, the insurance policy has still done its job: cover a non-intentional loss.
I would nevertheless advise you to have a look at what sort of homeowner policy your dwelling is covered under. Everything beyond HO-1 is nicer, and some even include limited claim forgiveness of some kind (for a price). Also consider talking to your insurance agent, who should be able to help interpret how the policy applies.