I looked (quickly, and therefore poorly, I'm sure), but I couldn't see anything in the ourworldindata sources that tries to distinguish the quality of forest left. I'm likely missing something, admittedly; I'll keep looking, if I find a link to their methodology I'll post an update.
They seem to be gather data from the UN FAO forestry project, and also other sources. I still haven't found any in those sources that account for the size of the trees; but ourworldindata does indirectly include some evidence that size may have reduced - the UN FAO source estimates forest coverage has dropped by almost exactly a third; but the tree number (where tree is defined as being 10cm in diamater at breast height) has fallen by almost half. However, since the sources use wildly different methodologies, I'm sure there might be other causes for the discrepancy, but in any case - it still highlights that interpreting these numbers isn't entirely trivial.
(Incidently, the same caveats likely hold for the globalforestwatch.org site; there too it's not obvious what they're actually measuring, nor how well they can do that, nor how close whatever metric they've got aligns with whatever you actually care about.)