The abandoned car outside the cabin
I've seen references over the years to tweets from ED13 director Fede Alvarez, saying that the car falling apart outside the cabin IS supposed to be Ash's car (with the fact that it's actually a '74 Delta, whereas Ash's was a '73, being down to what was available). I've never seen those tweets (I've never been on Twitter) but it seems to be accepted.
So I guess Alvarez intended ED13 to be a direct sequel to TED, ignoring ED2 and AOD (obviously, if he'd included those films the car couldn't be there). I actually have a vague memory Alvarez may have said something along those lines at some point.
Edit: Okay, I found an article from 2018 that quotes Alvarez's tweet https://movieweb.com/evil-dead-reboot-sequel-debate-answered/
On Twitter, Fede Alvarez was asked by a curious fan if the film is a remake or a sequel, looking to finally end the long-running debate. Straight from the director's mouth, the 2013 film is apparently a sequel to the Bruce Campbell movies. A dead giveaway, as pointed out by Alvarez, is the inclusion of Ash's Oldsmobile, which can be seen in the original films (as well as virtually every other Sam Raimi movie). This was previously thought by some to be a mere Easter egg paying homage to Ash, but Alvarez is clarifying that this is intended to be the very same car. Furthermore, the similarities between the 2013 reboot and the originals were designed that way by fate.share
"It continues the first one. The coincidences on events between the first film and mine are not coincidences, but more like dark fate created by the evil book. (Ash car is still there rusting away.)"