Their lost years- Elsa and Anna had like 15 years apart, I think? After being incredibly close as children. Luna and Tia had a 1000 year gap that also hindered their relationship.
When they meet again after that lost time- Elsa accidentally reveals she has magic and runs away; Luna returns as Nightmare Moon and has to be redeemed before she can reconnect with her sister.
I dunno, maybe it's just me, but these sibling duos remind me of each other.
Based this drawing off of a Frozen 2 screenshot where Elsa and Anna are touching their foreheads together, a gesture I have always found very sweet. You can find that image here.
I like to think Celestia and Luna become as close as Elsa and Anna are, not necessarily relying on the other for happiness (like Elsa and Anna seem to do with each other), but more in a way where they're balancing each other out. They are sun and moon after all.
I also like to think they're adopted siblings, or were raised as siblings after being handpicked for alicorn ascension at very young ages. They just look so different from each other that my brain sways from biological siblings to adoptive, but then again pony genes seem to be pretty random (Pinkie is an example). Either way, I like to think that Cadence and Twilight are the next set of "sisters" to come after them, Cadence being the one to inherit the role of raising the sun, and Twilight the moon.
Speaking of that, Celestia's original heir was supposed to be Sunset Shimmer, but when she proved to be too power-hungry and narcissistic, Celestia banished her and chose Cadence as her next "heir" instead. Cadence obviously has no elemental connection to the sun, but it seems fate was on Celestia's side, because without Cadence the Crystal Empire would never have been rediscovered.
Another headcanon I have is that Celestia's mane was entirely pink before she banished Nightmare Moon. When she banished Luna, she knew she'd have to absorb some of her magic to be able to raise the moon since Luna wouldn't be able to anymore. As a side effect, her mane changes color and adopts some blue in it (but she still has the original pink in there). Similarly, Luna's absorption of Nightmare Moon leaves her with permanent dark splotches all around her body, and her once feathery wings turn into bat wings. The change sticks even once she is freed from Nightmare Moon.