I've taken a look at this list of constructed languages, and there are indeed a few ending in -i, but it doesn't seem to be common.Is it just my impression, or did this suffix become quite common in English to form names of languages and peoples in fantasy ("Dothraki" comes to mind, but I'm pretty sure there's more)?
It's also a part of Indo-Aryan usage as an inherited form from Prakrit and as a borrowing from Sanskrit, Persian, and Arabic. The word "Bangladeshi", for example, is composed of "Bangla" + "deshi" where the -i (-ī) is a regular New Indo-Aryan continuation of Sanskrit -īya.Don't worry, it's common Semitic and further Afro-Asiatic, cp. ישראלי - Wiktionary & עברי - Wiktionary.
Not sure about Indo-Aryan languages, but in Persian/Dari/Tajik a homonymous suffix with the same meaning is inherited: Old Persian -īka > Middle Persian -īk>-īg > New Persian -ī > Modern Persian -i, e. g. "mountainous" *kaufīka (from کوه - Wiktionary) > kōfīk > kōfīg > kōhī > Tajik кӯҳӣ (e. g. Кӯҳӣ in Russian, translation, Tajik-Russian Dictionary - Glosbe).