iPhone not turning on, not responding to hard reset, not responding to charger

I would get a quote and send the device in to a microsoldering capable repair shop. These are highly specialized and not the typical, fix broken screen type shops.

They can and will fix liquid damage / no power on situations as well as make the system healthy enough in a lab setting to get you your data back and not spend even more money fixing it to run permanently.

• https://www.microsolderingrepairs.com/blog/iphonedatarecovery

No power / data recovery are generally less than $250 for non-liquid damaged phones and maybe double that if there is liquid damage / corrosion to be remediated.

You’ll possibly pay more than going to shops like you visited, but the more capable shops have much more expensive tools and skills and can recover data that’s far too gone for a place that specializes on the easy repairs. These sort of shops are generally less expensive than full blown data recovery shops, but you might get a couple quotes before sending it off - just be sure what diagnostic fee you owe and when you are charged if they do or don’t get your data back.