But of a random question, but do we know whether Erysakes would be considered a nothos like Teucer? I'm curious since most of the focus in the Ajax is on Teucer and Tecmessa's status after hus death
I actually recently read an article that argued (among other things) that Eurysaces and Tecmessa are sort of retroactively legitimized by Ajax's death-- while Ajax is alive there's the possibility that he could marry a higher status Greek woman and have legitimate children by her, which would classify Tecmessa as a concubine and Eurysaces as a nothos born to a foreign slave, but after Ajax is dead it's clear that Eurysaces is his heir, as the only son he's ever going to have, and Tecmessa is the mother of his heir and therefore his wife and widow. The article was pointing out that a lot of Tecmessa's actions in the second half of the play take the form of playing the role of the legitimate citizen-wife in order to reinforce her son's status as Ajax's heir.
So their status in kind of limbo while Ajax is still alive (and at Troy). If he lives and goes back home to Salamis and has children by a free Greek wife, then Eurysaces would be a nothos, displaced by a legitimate fully-Greek half-brother the same way that Teucer is a nothos because Telamon already has Ajax, a legitimate fully-Greek son, and incidentally the same way Medea fears her children will be displaced by half-brothers born to a Greek woman. A son isn't a nothos unless, or until, there are more legitimate half-brother claimants, and Ajax's death ends the possibility of there ever being any other claimant to displace Eurysaces.
And of course all of this is in the context of the citizenship laws of Pericles about Athenian citizen children having to be born to an Athenian citizen mother as well as an Athenian citizen father, which don't strictly apply to mythic settings, but the issues are very much present, especially since Sophocles frames Ajax and Salamis as very Attic/Athenian.
(Ormand 1996, "Silent by Convention? Sophocles’ Tekmessa," AJP 117, jstor.org/stable/1562152)