On paper, Mathilde speaks Tar-Eltharin. In reality, Mathilde speaks Teclis-Eltharin plus two centuries of an unknown amount of Grey Order drift. Mathilde speaking Eltharin would probably sound odd to literally everyone but other Grey Wizards. And 'Tar-Eltharin' itself probably doesn't exist - Ulthuan has ten kingdoms, has had eleven Phoenix Kings from six of those kingdoms, and has the Everqueen providing a cultural counterbalance, which would prevent any regional dialect from achieving dominance. The closest thing to a 'pure' Tar-Eltharin would probably be the Lothern dialect: a blend of the Eataine dialect with influences from Avelorn (from the Everqueen) and Caledor, Yvresse, and Saphery (from having supplied eight of the Phoenix Kings). But Teclis is from Cothique. 'His' accent, and therefore Mathilde's, would probably be more familiar to Marienburgers than it would be to Lothernites.
Yen-Eltharin would probably be a lot closer to the Eltharin of the Golden Age than Tar-Eltharin. Laurelorn is very isolationist, has had only four leaders, each of which was raised by their predecessor, and has a very concentrated population, all of which makes for a lot less cultural drift. The only 'foreign' influence would be fragments of Forestborn slang leaking through.
The written script of Eltharin is logographic, and so the original lexicon would be unchanged, but there would have had to be a lot of additions over the years for neologisms. This would probably be the biggest obstacle to communciation between the different Elven populations - for each concept that the original Eltharin didn't cover but has needed covering since then, each of the populations would have had to decide for themselves whether to ignore it, describe it using existing words, or coin a new word and therefore new character for it. The modern Yen-Eltharin lexicon is probably noticeably smaller than any of the other dialects due to their isolationism reducing the amount of new concepts they would have encountered and needed to coin words for over the years.
But despite all that the dialects are all mutually intelligible, and Mathilde would be able to understand and be understood by speakers of any of the dialects. There just seems to be less linguistic drift in the setting than in reality, possibly because of pretty much all the languages having either Old One or Daemonic or both in their bones, and so the words aren't arbitrary sounds that have been assigned meaning pretty much at random, they carry a hint of genuine conceptual resonance that gives the languages more sticking power.