Here you can find an assortment of music from various styles arranged to fit the range of different kinds of ocarina. Many of these have audio as well as sheet music.
Jack Campin's 9 note tunebook is a collection of more than 600 folk melodies from many cultures around the world. And all of this music works great on the ocarina.
The book is available for free in two formats:
This music fits into a range of just 9 notes - with a few sharps / flats, suiting an ocarina in C at notated pitch, and can be played on ocarinas in other keys if transposed.
A collection of Scottish music for G ocarina put together by Jack Campin for the 2024 Budrio ocarina festival.
These are some historic (19th century) compositions for the ocarina, including piano accompaniment. These are not easy, and generally range between about grade 4 and grade 7 in relation to the ABRSM flute syllabus.
I have compiled a tune book with a wide assortment of Irish tunes that suit a single chambered ocarina, which includes some guidance on playing style:
If you have a multichamber ocarina like the Pure Double alto D, the entire repertoire of Irish music is open to you. I'd recommend looking at thesession.org, an archive of thousands of Irish and other folk tunes, all completely free.
Bagpipes and ocarinas both have a limited range, and thus a lot of bagpipe music is easily adapted to the ocarina.
It is worth noting that bagpipes are not limited to the highland bagpipe, many different kinds exist, with sounds ranging from loud and strident, to soft.
While not strictly idiomatic (the ocarina is a 19th century instrument), a lot of medieval and early music can be easily adapted to play on the ocarina.
The "living history tune books" are a good starting point, including music and notes about their original use and origins where known:
Emiliano Bernagozzi, an italian ocarina player, has published a number of arrangements for ocarina Ensemble, available from:
https://www.sheetmusicplus.com/search?Ntt=Emiliano+Bernagozzi