Ok so I also wasn't able to find the font but I have some extra information that might be helpful. I ripped some assets from DtP a while ago, including the cutscenes. I can tell that the text isn't part of the video file, but is rendered in realtime on top of it. This might mean that there's actually a whole font for this stored somewhere in the game data. The bad news is that it would be stored at the resolution that you already see it at, so that won't let us get a higher res version unless there are some extra characters that aren't visible that would help with identifying it (There's also the possibility that the whole message is stored as a single image, which wouldn't help us much except maybe for being a little less blurry... either way, neither a font nor the whole message shows up in my rips).
I seem to recall some similar looking cursive showing up in Moonlight Museum, but that's gonna be way low res considering it's on the WonderSwan.
Normally I would say that if you want something from DtP but in a higher res, the WiiMake is a good place to look; for some reason, though, that message is completely omitted from the WiiMake's credits... I can't think of any other place in either DtP or the WiiMake where that font is used, but if anyone else knows, more characters to base things on would be helpful. (I already looked at the intro cutscene, that uses a non-handwriting font).
I tried to clean up the image to make it easier for those automated font identifiers to use. I was able to find a sort of similar font with the automated sites called "Datho Ostma," but it has a few issues. First, it costs like $15. Second, its from 2018, so it's definitely not the actual font they used. Third, the lowercase 'f' looks completely different. I'll upload my edited version in case anyone else wants to try with it.