Not sure if character/ship playlists are still a thing in fandom but I love making them.... Here's the anieuphie playlist I started last year, I revise and update it often tbh. It's songs that remind me of them!
I ended up rambling about volume 7, as it's one of my favorites but I rarely see anyone mention it. I always find myself coming back to that volume and rereading it. It's a great break between 6 and 8, while providing very solid character development. overall I wish more people would read the novels past vol 3 / after watching the anime. they're really good!!!!!
In volume 5 we are introduced to Clive, Orphans's retired butler and retainer of the 3 children who grew up among the royal family, including Euphie for her assignment as future queen. Despite his retirement, he volunteered to oversee Algard during his exile.
The way in which Euphie and Anis both greet Clive is very nostalgic and it seemed they knew him well. Anis remarks right after that however that he'd been in retirement for around 10 years.
If we do the math, considering vols 4 + 5 combine into almost a year's gap since vol 3, that would make everyone around a year older in 5.
Which, if we subtract 10 years from, would result in Clive's retirement happening when Anis was around 8, Algard and Euphie around 6.
Since Anis mentions that Clive was responsible for Euphie's preparations as queen, it implies that her assignment as one was done at a very young age. That, and I'm not sure if it was decided before or after Anis denounced her right to rule, since Algard was already ahead in preference.
It also raised the question of why Anis and Euphie weren't very familiar by the beginning of the story, seeing as they've had plenty of chances to be around each other as children (Anis mentions going with Algard to play at the Magentas' estate before Euphie was assigned future queen, and now this case of them most certainly sharing some of Clive's tuition and attendance).
My theories would be:
Even though they interacted, Euphie's reserved nature and her observation of Grantz made her feel too uncomfortable to address Anis and Algard by anything less than mega-formal. That included her interactions with both of them, which likely made her feel less in a playdate and more in a meeting where her steps were watched. Which is crazy mental work for a 6 year old, perhaps even younger
Although she shared some tuition with Euphie, Anis simply ditched her classes under Clive or otherwise. Even though we know she was supposed to take them, at least before she ditched her right to the throne, perhaps she gave up altogether and knew there was little consequence. Or, well, maybe they weren't shared classes at all. But I thought Anis implied that they were.
Anis's behaviour was seen as negative influence on Euphie, and as such they were unfavored to interact. This comes from a side story in the web novel where Ilia chases after the younger royal siblings who had tried to fly down the stairs. The scene happens while young Euphie is accompanying Grantz, who orders her not to look at the ruckus when she shows bewilderment.
TLDR; Euphie was friendless and carrying insane weight at the age of 5. Which explains some things. I guess.