Since this scene is never actually shown to us in the game but rather is only something we're told about second-hand, the exact/finer details of what the memory entails is... entirely up to me as a player to decide. This is quite convenient as a starter memory because it quite neatly allows me to pick and choose what bits of information I want to have Furina remember (or not remember) at this point in time, according to what I feel will be the most interesting to play with.

However, it's also quite inconvenient in a way, because I have no record to refer back to as to what I've decided would be reasonable details for her to remember. So I'm putting a write-up here to help me keep my head on straight about what I've headcanon-ed would be reasonable for Furina to be thinking and feeling during this memory, and what she could reasonably remember and intuit.

For the record, I've started the memory from Furina arriving at the party and sectioned off the earlier part of the story (Clorinde showing up at Furina's house) into a different memory fragment, because it would contain more information than I'm comfortable giving Furina for her first memory. So, for posterity, here we go.

Just the facts: What do we know happened?
Furina showed up to a party she was invited to, feeling anxious that the people there wouldn't want to see her. Once inside, she was initially quiet and reserved, unsure of how to proceed. However, it turns out that Furina is a tremendous light-weight, and within two drinks, she forgot her anxieties and became the life of the party. A fun time was had by all, and this is the first time that Furina had ever experienced a night of drunken revelry with her friends.

Headcanon: Who would have been at the party?
Officially, the anecdote only says Clorinde. However, it's a party, so it's reasonable to assume others were there as well. I'm ruling out Neuvillette, Wriothesley, and Arlecchino, as it doesn't seem like their scene, and I think we would've heard about it in the story if any one of them had been there. Charlotte, Lyney, Lynette and Freminet all don't seem like they run in the same social circle, so they're out as well. That leaves Navia, Chevreuse, Chiori and Emilie as known named characters who seem like they would attend a party with Clorinde, so for simplicity's sake, let's say they were there, and some other unnamed NPC friends.

Headcanon: What would they have discussed at the party?
I've been treading lightly around this topic in Furina's threads about what she remembers, even though the game will never contradict me, because I honestly just don't want Furina to remember too much about herself at this point in time.

I think it's reasonable that Navia and Clorinde would have spoken positively about the Poisson recovery efforts going smoothly (something which current Furina has no context for other than "I guess a disaster happened?"), and I also think it's probable that someone at some point would have asked her what she was planning to do next, to which Furina would have given a noncommittal answer, since she wouldn't have known at this point in time. (The story seems to imply heavily that this took place prior to Furina's story quest, so she hadn't gotten her vision yet.)

Other than that, it's a bit strenuous for me to create wholesale from cloth all the possible topics of conversation that could have come up at a party, so I've been handwaving it as "Furina spent the time she was sober at the party too absorbed in her own anxiety to pay close attention to the conversation, and once she got over her anxiety, she was drunk, so her memories of the finer points of the actual conversations are rather fuzzy. What she remembers more strongly is what she was thinking and feeling."

Headcanon: So, how might she have been thinking and feeling?
We know from the story that she was quiet and anxious at first, and then merry and exuberant after drinking, and that it was the first time she'd experienced drinking with friends at a party. So although it's an overall positive memory, amnesiac Furina doesn't know quite what to make of it, and she's still trying to puzzle her way through it.

What she does remember is feeling anxious about knocking on the door before entering the house. She remembers being afraid that her presence may not be wanted there, that the others may not want to see her, that they might hate her now for something she'd done-- but she can't remember what that thing is. She knows it's big.

What she remembers is feeling overly self-conscious of how she conducts herself in a room full of other people at a party. Unsure of how she should act, unsure if she belongs. Feeling keenly that the way she "used" to act is inappropriate here, but not knowing what the correct way for her to be in this situation is either, because she hasn't quite found herself yet.

I did want her to remember what visions are, so I headcanoned that at some point before the drinks happened, she would have been staring at Navia and Clorinde with their visions, and feeling a little bit envious of them. Not in a mean way, just in a way of feeling like... "I wish I were more like them." At this point in her life, Furina's whole world has turned upside down, and she isn't sure who she is anymore. She's keenly aware that she's never had a vision because she's never had an ambition for herself-- she's only ever done what she was told to. So I think it's natural for her to feel a little bit wistful of people like Navia and Clorinde, not because they can wield the elements, but because they seem like people who have it all figured out. They're full of natural confidence and poise, and seem to know exactly what they want out of life.

What she remembers feeling later is exuberance and joy once she gets a little tipsy, and further joy upon realising that her friends don't hate her at all, that people want her there, and that this is fun. I think it would be reasonable to assume she would feel a little bit wistful and think something along the lines of "I never knew this could be so fun," or "I should have done this years ago." The story makes it clear that although she still doesn't know what she wants to do with herself from here, she knows that she enjoys being social with others, and that even in her worries and depression, social isolation isn't the way to go.

So, what does Furina in Tributary make of all this?
Funnily enough, depsite this being an immensely positive memory for Furina in game, Furina in Tributary... doesn't think all that highly of her past self from this memory alone.

Without the knowledge of the rest of her life to put this memory into context, Furina in Tributary remembers this one scene and thinks of her past self as someone who was lost and a bit sad. Someone who needed to get drunk before being able to be herself at a party. Someone who was overly concerned with what other people thought of her. Someone who desperately wants to reinvent or find herself, but isn't sure how to do so. Someone who feels... well, a bit useless, really.

But she knows that she enjoys the company of others, so for now, she's following that feeling.