Anime

I remember when I first watched Little Witch Academia and I had basically this exact same thought, especially when the intro and outro changed mid-series. Then I watched Azumanga Daioh and I had the exact same thought again, and found it a bit odd that both of my first two anime would happen to both have such long intros. Then I watched Aggretsuko and I didn't have this thought because that show's intro was a "normal" length. And then I watched Girls & Panzer and I started thinking that it was probably not a coincidence that 3/4 anime I'd seen had an intro and outro that was exactly one minute and thirty seconds long.

Indeed, 1:30 intros is basically an industry standard for anime and has been since at least the 1970s I think. How it works now is that a musical artist or band makes what they call a "TV size" version of an intro/outro (which they refer to as the "OP" and "ED" for "Opening Theme" and "Ending Theme"), which is always 1:30 long, and simultaneously they make a full-length version of the song. This is basically a way for the J-pop/J-rock and anime industries to mutually reinforce each other through collaboration, or sometimes the full-length songs are sold as merch, I think. So for example Frieren's opening theme was made by Yoasobi who are a super popular duo who also made the opening themes of Beastars and perhaps most famously Oshi no Ko: Yoasobi gets to plug the anime to their fans, while the anime get to plug Yoasobi to their fans.

How the anime industry landed on 1:30 intros in particular I'm not quite sure, but I think it's basically just what naturally worked the best for the typical song structure. You might notice that at the "peak" of every anime intro/outro that you'll see some text between these brackets 「」 — those are CJK quotation brackets, and the text betwixt them is the song title.