In Hindu India I'm not sure if people were doing science in Sanskrit, Prakrit, the vernacular - or even Persian?
In Hindu India specifically? Mostly Sanskrit, which remained the language of formal treatise in science, literature, and (especially) theology. The works of Kerala school, for instance, which flourished between the fourteenth and sixteenth centuries and focused on astronomy and mathematics, were mostly in Sanskrit - such as its foundational text, the
Tantrasangraha by Nilakantha Somayaji. That being said, commentaries on these texts were sometimes written in the vernacular; the
Yuktibhasha by Jyeshthadeva, which is a commentary on the previous text, was written in Malayalam (and is, in my opinion, the more important of the two, since it semi-rigorously proves theorems on infinite series conjectured in the former). All of the formal
Navya-Nyaya (lit. "new logic," basically a philosophical and epistemological school) texts were also in Sanskrit, though again commentaries were written in Bengali, which was the local language where the school reached its zenith (though note that that region was under Muslim rule).
Overall, then, you might expect things like commentaries or didactic prose and poetry (such as in astrology or medicine) to be written in the vernacular. Some local traditions could also have their formal writing be in the vernacular -
shiddha, which is a traditional form of Tamil medicine (and complete quackery) had its technical writing in Tamil prose or verse. Some religious texts could also be written in vernacular, such as the Lingayat tradition mostly having its works be in Kannada, though these were on the whole mostly devotional poems, not analyses of Vedic theology.
Since you brought up Persian I may as well cover Muslim courts. In these, depending on the particulars of the time, both Sanskrit and Persian would have been patronized (with the religion of the scholar determining the language of writing). That being said, going by the fact that much more Sanskrit texts were translated into Persian than the other way round, Persian was definitely the language of most scholars. And Arabic, mostly in law and theology. The major "Persianate" vernacular was Urdu, which emerged from various historical processes, but its literary tradition was born in the Deccan, after that
disastrous 1327 capital change (and un-change, though the nobles stayed). It was mostly literary, not scientific; some of the finest poetry from the period is in Urdu, especially under the sponsorship of the Bahmanis.
Also, a note on terminology: "Prakrit" is a weird word used to describe both the common Indo-Aryan vernacular languages between the fifth and twelfth c. and the strand of related literary languages that emerged from Classical Sanskrit were used during the time period. In our time period of interest, Prakrit is not a good term to use, since most of the Indo-Aryan languages are considered to have reached their "modern" stages.
Gameplay-wise, liturgical languages are designated by religion, so undoubtedly the system will fail to capture some of the nuance we have here, especially in the case of the sultanates. I am unsure what effect this will have exactly, since I assume all languages have "language power", but I do not know what that actually does.
Likewise in Southeast Asia - was Pali actually the language of intellectual pursuits or just of scripture?
Depends on where and when. Sanskrit would have been used in some places, especially pre-Islamization, before being replaced by Arabic. Though in strongly Buddhist areas like mainland SEA, definitely Pali.
