I presume this also applies to the Hebrew script.
I’m not sure that this is really the best place to target the Nominatim developers, but my guess is there are probably few, if any, of them with any knowledge of Arabic scripts. My impression, even for the map itself, is that mapping in many Arabic script using countries is done by European expatriates, and one of my general concerns is the overuse of the Latin alphabet, and even partially anglicised names, where those are not the primary scripts and languages used locally. (In some of the larger countries, mapping seems to be done by an English speaking intelligentsia.)
I’d therefore suggest that the first step is to get more Arabic/Urdu/Farsi/Pushtu users involved in OSM. From that pool, you should find a few interested in working on the Nominatim code.
Failing that, what is likely to be useful is references to standard texts (in English) and open source software, relating to the algorithms used for comparing machine readable Arabic script texts.
(Some examples of where you would expect to see almost entirely Arabic script, or at least dual Arabic and Latin, but don’t, are https://www.openstreetmap.org/search?query=pakistan#map=10/27.5679/68.3020 and https://www.openstreetmap.org/search?query=dubai#map=14/25.1774/55.2641 Iran seems to be the main exception, although Iraq also seems to be mainly Arabic, but with some exceptions.)
(As additional background on the issue here. Scripts for Semitic languages, in everyday use, don’t encode short vowels (a bit like English shorthand, for those old enough to remember, drops all the vowels). The consonants convey enough information for people to recognize the words, even though not enough to pronounce the word phoneme by phoneme. In more formal contexts, the vowels are fully encoded. I believe that is always the case for the Quran.
In Unicode, the vowel marks are coded as separate characters, and the font engine is expected to combine them with the base character.)