Like many others, I think she's drawn in by Emma's confidence and exuberance. She's a no frills, no bullshit kind of person, so while Emma does strive for the ideal that's seemingly out of reach and can entertain theatrics, she's carries herself with such conviction and earnestness that Ayshe can't help but respect it and eventually find it endearing.

Similarly, Emma appreciates Ayshe's honesty and how thoughtful she is. She's definitely not a talker in comparison, but Emma doesn't mind in the least that her love language is acts of service and physical touch. - Ayshe is more reserved with physical touch and prefers to do it in private, but if Emma tacklehugs her in public she isn't one to refuse, even if her reciprocation is more subdued. - One of the most poignant moments of this is them mutually caressing their scars (Emma brushing back Ayshe's bangs, Ayshe brushing back Emma's braid) - Ayshe is also very sensitive to scents, which frequently leads to her being the big spoon so she can nuzzle Emma's hair.

Despite being a no-bullshit kind of person on most matters, I can't imagine a scenario where Ayshe is the first one to verbally express her feelings even if she's the first one to consciously recognize them, so Emma would have to be the one to get them officially together with her Type A personality. Even after countless nights stargazing, trekking through the woods, finding themselves curled up on the couch together with the dogs, and just being in general proximity to each other, Ayshe still finds herself caught off guard and blushing when Emma asks her out. Emma thinks it's cute. <3

Speaking of the dogs, Emma the spiritual golden retriever absolutely adores them!! She loves rolling around with them, cuddling with them, taking them for walks, etc.

Ayshe didn't really get to know Emma prior to losing her memory, and Emma secretly takes comfort in that. They both have the baseline of what they hear from other people, and Ayshe has the few days they spent together in November 2047 for a bit more context, but there's a greater degree of separation between the Emma who lived in the demon world and the Emma of the present for both of them that Emma subconsciously gravitates toward when she's in a guilt/shame spiral during the first few years after their reunion.

There would be an axe-throwing/knife-throwing/darts date at some point. Emma would be boisterous in her boasts of prowess while Ayshe would match her in pointed, confident smirks. Despite both being competitive about it, neither really minds losing since the prize is a kiss (and then some).

(Chapter 139)

After she just told them Norman was behind her father's murder—someone who was her whole world—they're in tears at the thought of not being in conflict with him. Even when considering the possibility that Norman ultimately plans to kill Sonju and Mujika after they bring them to the paradise hideout, if there's a chance of negotiating with him, they'll take it.

It goes even further when Norman betrays them and uses them as bait just like they suspected in chapter 135.

(Chapter 144)

Gilda still pleads with Mujika, after Norman just tried to have her and Sonju—her companion of 700 years—killed, to help them stop Norman before things become irrevocable for him and everyone around him. She still considers him her older brother after all of that. Don looks empathetic and in agreement with her while Ayshe is left in open-mouthed shock, because she could understand if Gilda didn't want anything to do with him at this point.

But she also understands family, and her new companions have made it clear that her father's murderer is still important to them. She doesn't begrudge them for it.

(Chapter 167)

And she doesn't hesitate to save them when they return to Grace Field.

She has known them for ten days.

(Mystic Code Book Chapter 7)

Within the span of four days, she's willing to have this conversation with Ray:

(Chapter 169)

This is after Emma has made it clear how close she and Ray are with Norman:

(Chapter 161)

She's conciliatory to Don and Gilda when she says "it's true that he ate humans, but to me, he was my father" and here. Despite acknowledging that familial connection she feels toward him, she gives all of them an out. 'You don't have to spare my feelings. I understand why humans hate demons.' Knows most demons wouldn't think twice about eating her if given the opportunity. She's downcast and gives a light sigh of resignation because she's aware of how bizarre this would look to another human. They can conceptually see why she feels the way she does, but not how profound that loss is for her, so she'd rather skip the attempt at sympathy.

It's why she's so shocked at Ray's blunt declaration reaffirming her love for her father as valid and gives her full attention to him in earnest. She follows it up by saying their parents were also good people.

Given their prominence in the story since the start, I'm fairly confident the figures on the left and bottom center are Norman and Don respectively so all five of the oldest Grace Field kids are included here and poignantly attached to her sentiment. It's possible she's lying to Ray to be reciprocally kind or mentally separating the kids into differing levels of good with Norman at the bottom to still technically qualify him, but with less reason to lie to him between the validation of her feelings and the intimacy of the setting I'm disinclined to believe the former, and with the latter he's still included regardless.

(Chapter 181)

With all that in mind in addition to how she's willing to let Norman and Vincent hold her dogs' puppies post-timeskip, it would be very bizarre for Ayshe to hate Emma. If anything she'd think Emma's too good for Norman lol

I also imagine there would be a lot of overlap between how she interacts with Emma and Ray.

(TPN Light Novel 4: Films of Memories - “Don and Gilda”)

She reacts this strongly to Don and Gilda even thinking about being burdens in the post-canon. Despite lacking those memories, there are still convictions she holds that are etched into her very being. If she was given a rundown of Ayshe's history, she'd also conclude that her father's species was irrelevant if he saved her and provided her with unconditional love, possibly more forcefully than Ray. It wouldn't come as a surprise to Ayshe, given her interactions with all the other Grace Field children at this point, but it'd be comforting all the same, that reinforcement of why Emma's friends and family cared so deeply for her and spent years searching for her. There was never really tension between them, but it makes Ayshe feel more at ease around her all the same.