Aha, you were right, I figured out the problem! After enabling artist split, you need to do a "Full Rescan", not just a standard Rescan - then it shows up like in your player. It had nothing to do with tagging (I tried adding a space before and after ; in a file and it doesn't make a difference)
However, now I've got the opposite issue, I actually liked having both the groups and artists showing up in search 😄. E.g. in your example, you've only got "Olivia Newton-John" showing up in Artist when you search for olivia, but it's convenient to also have "Olivia Newton-John; John Travolta" showing up, because then you can quickly select all the songs with both Olivia and Travolta as artists, and exclude songs with only Olivia as the artist.
So I guess that's my new feature request: In the search results, please show every multiple ARTIST field of songs containing the artist you searched for.
Oh and thanks so much for taking the time Andre!