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I would think it would depend on whether the material the light hits inside the window reflects UV light, or absorbs it and re-emits it as heat.
Even if it reemits heat, some will be lost to air via convection and half goes wrong way
Less than half, because glass isn't a great heat conductor.
That’s true of any material that gets warmed by sunlight, though.
Slightly. Most of solar energy comes in as visible light, so any visible light that gets reflected won't contribute
No. The UV light is on the other side of the rainbow from the light that makes you feel warm: Infrared.
Infrared is the peak of the frequency range emitted by objects that are roughly body temperature—that doesn’t mean it’s the only frequency that makes objects warm.
In fact all light that isn’t perfectly transmitted or reflected makes things warmer.
Yeah I think my microwave has something it wants to say
Is it "mmmmmmmm"?
at 2 am: beep beep beep
That's false. You can literally not only feel heat from, but you can in fact set things on fire with, a completely monochromatic green laser with a wavelength exactly in the middle of the visible spectrum. No infrared, no ultraviolet. Lots of heat transfer. You could do it with an ultraviolet laser too if you were careful enough and could get around ultraviolet's tendency to destroy molecular bonds completely before they even have a chance to burn chemically. It's not just lasers either, any light source is going to deposit energy in the form of heat on anything that light touches. Any light contains a large amount of energy and some of it will get absorbed by anything it interacts with, and that's still true whether it's infrared, ultraviolet, somewhere in between, or all the above.
Infrared has a special relationship with heat, yes, because of the distribution of blackbody radiation, but "No" is absolutely the wrong answer here. The right answer is "Yes, but... it's complicated".
This is correct but also glass blocks both ends of the spectrum. Really just visible light goes through glass. You get some near IR passthrough but not much.
There’s glass that doesn’t block UV frequencies—like the glass used in tanning booths, UV lights, and UV cameras.
You should look for semi-reflective or tinted glass if you want it to not let warmth pass in to your home. (And if you have double glasses, only the external one should be treated.)
The UV-blocking glasses will warm you less, but as you noticed, not enough to make a sensible difference. They add absorption of a very small band of light that isn't the most intense on Sun-light and is also absorbed by the atmosphere.
It definitely heats your DNA less!
Not sure about how it feels on the skin, but here's a good explanation of how Low-E glass coatings keep homes cooler in the summer
https://glassed.vitroglazings.com/topics/how-low-e-glass-works
Ever drive in a car?
Roll the window down on a sunny day, you'll feel the difference.
It's not a massive difference though.