Is there any accessory which would let me charge my iPhone and listen to 3.5 mm headphones at the same time

This is probably what you're looking for:
https://www.amazon.com/Splitter-Certified-Lightning-Headphone-Compatible/dp/B00TZIW41G

If you already have a headphone dongle, then you might want to just get a splitter, though.

I have such a device. I have no idea what it's called because I got it some time ago from Amazon. It has a lightning cable to connect to my phone, and then a port to plug a lightning power cable into, and a 3.5 jack for audio. I wish I could give you a name, but perhaps knowing it exists will help you continue your search.

Just to mention, if you have a wireless charging capable iPhone, such as 8 or newer, you can set it on a wireless pad and plug in the lightning dongle. There are even portable power banks with Qi charging. Or use the adapter the first commenter mentioned.

You can find the Belkin RockstarLightning Audio + Charge on Amazon.com. I use this device and it works very well. The product is sturdy and well-built, as well. Highly recommended