Yeah, it’s uncommon, but I’ve seen that そら reading used in other places too, but it’s mainly been in manga, anime, videogames, like in your example.

I wonder if it was a relatively recent fad to read it that way (like in the past 20 years or so?)

In the visual novel 9-episode, there’s a kind of a meta comment about that unusual reading.

One of the characters in the visual novel is a teenage girl who was born with the 天 name and そら reading. She intensely hates this name because because everyone usually just calls her てん instead of そら. She describes her name as a 厨二ネーム and she blames her parents for trying to be too edgy, like a 中二病 teenager edge-lord who has read too much manga and comes up with cringe-worthy names thinking they are cool-sounding but they are not.

Because of that 厨二ネーム, she thinks that’s the reason why she’s grown up with an eccentric personality, and does strange goofy things, all because of the edge-lord-sounding name. She vows that when she becomes an adult, she’ll change her name to something more conventional.

The 9-episode visual novel came out a few years ago, so the girl’s parents might have grown up reading manga like Bleach. so I wondered if this was a kind of meta-joke on chuuni-souding names with weird readings.

I laughed when I read the teenage girl’s rant about her name because 厨二病 / 中二病 is something you usually attach to teenagers, but here, the teenager is criticizing her adult parents for being like that, so it’s a kind of role-reversal.