I have installed the latest BIOS for the dock and the computer, but the laptop comes up with the warning that the power output is only 130W. I've tried other docks and power bricks and outlets, but the issue remains. The same docks and power brick work fine. I've seen this a couple of times, but there never seems to be a concrete answer.
Here's your concrete answer: The TB16 can supply at most 130W to attached systems, which requires the TB16 itself to be powered by a 240W adapter because the dock itself consumes some power and needs to keep a reserve available for an "upstream" Thunderbolt device you might plug into the Thunderbolt port on its rear. 130W obviously isn't enough for a Precision 7000 Series system, which is why the System Compatibility Matrix table on the TB16 FAQ page here has a row that says "Precision 15 7510 (requires system power adapter for charging)". Technically the official max of the USB Power Delivery spec is 100W, so Dell is already doing something proprietary to stretch that to 130W.
It seems there's also a new Dell TB18DC specifically meant for charging Precision 7x30 Series systems here. However, it requires that the system have two Thunderbolt ports and that you be willing to lose both of them to a docking station. But for a 7510, you'll need to connect the system's AC power adapter even when docked to the TB16.