He used international dollars, which might be precisely what you’re looking for, in his last article (https://ourworldindata.org/extreme-poverty-in-brief) it is unclear if he used the same metric or not this time but I’d be very surprised if he didn’t, specially considering he references his old article several times.

And I wonder if that metric that accounted for parity in the power in purchasing (let's call it PPP for convenience), if it existed, would be much more than a crude bureaucratic misrepresenation of the situation on the field and bad government statistics taken at face value...

I'm not aware of a metric that accounts for purchasing parity between say Edinburgh and Gairloch