I have 12-speed Ultegra and love it. I did a gravel ride recently using my GRX mechanical for the first time in months. I ordered the GRX Di2 groupset for that bike the next week. I didn't noticed Di2 being so much better when I started using it. Rather I noticed how much "worse" mechanical was when I used it again. And of course, the mechanical wasn't really "worse" but you really notice how nice the Di2 is when you don't have it.
As for feel, again, I can only speak about the Ultegra 12-speed. There's no issue finding or feeling which button/lever to click. It has a click feel to it and there's no ambiguity to it. Though I do find the little auxiliary buttons on the tops of the hoods to be a bit small and hard to press. I use these to switch Gamin displays. But I noticed on the GRX shifters, the buttons on the hoods are completely different. So, clearly they vary how they work between groupsets. For example, if I were trying to choose 105 vs Ultegra Di2, and the only reason I was considering Ultegra was that 105 doesn't have buttons on the hoods, I would likely save the money and go with 105.
Charging is a non-issue. I can go about 6 weeks between charges. So, I just do a charge at the first of each month to keep an easy to remember schedule. Just like my weekly charging of lights and my Garmin. There's just no reason to intentionally run the battery to a low charge state.
It also charges pretty fast. I think probably from half to full charge in 2-3 hours. So, if you wake up one morning and remembered you forgot to charge it overnight, you could throw it on charge and get plenty back into it for a ride you might start in an hour or two.