...poorly? poorly. she never gets outwardly fussed about them, though she has admitted on retrospec before to being unsettled by the other elizabeth (particularly early on)
elizabeth is on the side of "maybe we were/are those people, but that doesn't mean we are those people, because the experiences we've had are different and have affected us differently" and she tries her best to sort of view them as, like
...guidelines, i guess. you learn from the past, but your past doesn't define you, etc etc. (despite that she's very firm on keeping to her present life's past, just because it's made her who she is today)
memory regains aside she actually finds the idea of being a summoner incredibly exciting, though she was very... she was worried, having thanatos as her sole persona for so long, that maybe destruction was the only thing she was good at?
...elizabeth, though, doesn't talk about her memories that much, and she's fairly hesitant to do it even though hers aren't objectively that terrible. she doesn't ask about people's memories and she doesn't tell about hers and that works out really well!!
except for when she comes to little realizations like in this october thread with yato that she knows very little about him and that is upsetting, sort of, and actually she knows very little about a lot of her friends outside of as she knows them at present
physical-wise, she has her silver hair and gold eyes back, and the eyes were a little worrying but at least she immediately got to go to sena like "so guess who's joined you in silver hair club" which was... better.
items-wise she has her grimoire, which she actually loves (she actually really likes the summoning bit her other self has going on; she always picks classes that has a familiar and etc in games if she can) and
admittedly i didn't know how elizabeth would really deal with hers until, like, stuff started happening, and it really does depend in a way on what memory happens first?
at least he's a first year and doesn't have The Idol War. he just has The Idol Revolution and Sena-senpai Kidnapped A Kid And Tanked Knights' Reputation
elizabeth's first memory was... iirc it was either her dumping money into a fountain or playing on the playground at the shrine. either way she was so thrown off by how naive her other self was and she just went "nnnnnnope nah"
and then after, like, realizing people knew people in recolle that were in her memories, she firmly took the stance of not wanting to force relationships or have those forced upon her just because of what she might've had in her other life
tbh a lot of elizabeth's ideology isn't bad, per se, she just also tends to decide that it's better off not talked about and she just keeps it inside forever unless it's specifically asked about or brought up
which just leads to persona users knowing she's a velvet room attendant, so probably not human at all, and i don't... think.... anyone else outside of that knows that...
she feels so cool when she summons stuff so she doesn't make it a secret that she can do it she doesn't usually refer to them as personas and she'd never out any of her fellow users as people who can do that too, ofc
one of these days she'll be forced to acknowledge that minako's brother she is now acquainted with is her guest in her regained memories and it'll be a lot of pretending that doesn't exist unless she's cornered about it ahaha... ha........
the same thing goes for any velvet siblings that come in; she'll interact with them, sure, but she sure as hell isn't going to say anything about past lives being connected and all that
because, again, she doesn't want to force that on anyone and she doesn't want that to be forced on her either. she's worked hard to be who she is and such so.... she respects the same for everyone else as well