tl;dr: is USB charging via Thunderbolt port officially supported on Vostro 7510? Does Dell sell a USB-C charger?
I have used the Thunderbolt port many times to charge the laptop (Vostro 7510) while traveling in lieu of the AC port. This allows me to travel a bit lighter. I purchased a high-quality, 4-port, 100-watt USB wall charger (and 100-watt USB-C cable) so I could charge my phone, tablet and laptop as necessary. Because the Vostro uses a 130-watt input, I would sometimes see a "slow charging" warning, but this was not a big deal, maybe it would take 2 hours to charge instead of 1 or whatever.
On my last trip, however, it all went bad. Unfortunately I had to use the computer away from a plug and ran it all down to zero, such that the computer would not turn on at all. I plugged in the USB cord the laptop that night and assumed it was all fine, but the next day I realized it had not charged at all. Then when I tried again to use the Thunderbolt port to charge I could see that the small LED light next to the Thunderbolt was not coming on. I plugged in the same cable into my phone and it charged fine. Only the Vostro was not responding.