Until recently, wireless charging was not an option for my truck. I've been using the power port (formerly known as a cigarette lighter) with a device that has 2 USB female plugs. Even with 2 phones charging simultaneously I found the performance to be very good. I do not use the USB and USB-c plugs in the Infotainment system. Those might go to my kids in the back seat with an extra long cable so it doesn't bother me. They haven't complained yet, so I guess it's keeping their tablets powered up.
I don't use Android Auto. I tried it when I first got the truck, using the aforementioned USB port on the Infotainment console, and hated it. If something was wrong with the connection between the phone and cable it would become disconnected. Bumpy roads are good at that. Also, I prefer to use Samsung Music for all the songs (about 2,200) I have purchased and saved on my phone over the last decade+. The music service through Android Auto just not allowing me to enjoy all of my music.
Getting back to the topic of wireless charging, I recently installed the wireless charger in my truck. I have no issues with its performance. My phone charges up just fine while I'm streaming music to my truck via Bluetooth. I have a Samsung S21 Ultra 5G. It has a larger battery (5,000 mAh) than your s10e battery (3,000 mAh) and Google Pixel 5 battery (4,080 mAh). Maybe something is wrong with your truck? Maybe something is wrong with your phones? I dunno. I just know that I'm satisfied with how things are working for me.