Papyrus isn't made from reeds, but rather from a sedge. It holds up for a really long time in dry conditions and not so well in damper climates. Even so, papyrus was used in Europe as well as North Africa, though Egypt was the main supplier. On Toril, given they have a longer recorded global history, the use of papyrus in areas where it is not ideal is probably less common than it was in our own history. Parchment can also break down in damp environments, but holds up a little better than papyrus and is more readily available where papyrus sedges cannot grow or be cheaply imported. While sheepskin is traditional, other animal skins were used as well. Because there are thousands of years of generally known recorded history and mostly continuous civilization, it would stand to reason that barring a particular cultural reason, most places would have optimized their writing materials for their needs. Longevity is not necessarily always a need, though I imagine elves would prize this more than say, humans, so that they don't have to recopy the same manuscript every generation. The availability of magic and alchemical preparations will have an effect as well, but the economics of such things on a large scale will vary and are really up to the DM since none of the setting material I know of has ever dealt with it.
That said, there are far more options for writing than simply parchment or papyrus and reusable wax tablets were common for a long time amongst all classes of society on Earth. Birch bark, bamboo and cloth were all used. Keep in mind that paper was common in Asia in the ancient world and by the late middle ages had become the most commonly used writing material in Europe as well. If paper making exists on Toril it has likely had time to spread and mostly places would probably have paper mills. Paper in decent library conditions can last for upwards of five centuries, and it is cheap and can be made from the parts of useful crops that aren't otherwise utilized. Grasses, hemp and cotton fibers have all been used to make paper, so even the Egyptian flavored Mulhorand would have made the switch from papyrus for anything they didn't need to have last for millennia without recopying it. All this assumes details based on realistic advances and spread of technology is what you are after. If you are more concerned with flavor and broad strokes of culture: put papyrus in ancient world dry climate inspired places, parchment in dark ages/early middle ages inspired places and use paper for Asian flavored places and high middle ages/renaissance inspired places. Also, wax tablets and slate boards with chalk for everyone! That's my two pedantic cents at any rate.
