PCB Power Pad destroyed for TPS51125. Fixable?
It might be risky.

The chip uses the power pad as a ground pad, it has another pin for ground as well, but it is likely the chip is designed to have most of the current going through the power pad.

Beside heating issue (which might be fixed by adding a cooling to the top of the chip), the fact the chip might have improper grounding can create issue.

One of this issue can be improper regulation of the output voltage and in the worst case, generating a higher voltage than it should be and in turn can destroy further components.

A safest solution to fix this issue would be to order a step-down converter small enough so you can fit inside the laptop and with the appropriate voltage and current ratings. Find on the board some locations where you can connect the input, output and ground with some wires.