I would use "Indic", a parallel to "Indo-". There had been a political entity called India by the British, but it split politically into Pakistan, Bangladesh, India and Sri-Lanka/Celyon, so calling all such people "Indian" would be politically reductive.
It is very important to accurately name such peoples, as they are now the most numerous on earth with about 1 in 4 humans being residents, or descended from residents of the Indian Subcontinent.
I am not sure that South Asia is specific enough, since all Asian places south of China, the Caspian Sea or the Himalayas would most etymologically be "southern Asian". In the UK, where there were waves of immigration from Africa, home to generations of migrants from the old British India, I believe that the term "South Asian" was one of political correctness. The map below differs from my proposal in that a) it oddly puts Afghanistan and Iran in "South Asia" instead of Central Asia, and b) it oddly omits from West Asia former West Asian Soviet Union (Georgia, Azerbaijan and Armenia).

That in mind, there should also be reworking of poltically-imbued terms to reflect geographic reality and be geographically consistent. I propose:
"South-West Asian" (i.e., the Indian sub-continent and associated islands)
"South-east Asian" (Philippines, Indonesia, Malaysia, Brunei, Singapore, New Guinea and Indochinese nations).
"West Asian". The medieval term "Levant" or even the European-centric misnomer "Middle East" should be renamed "West Asia" to include Turkey, Georgia, Armenia, Azerbaijan, Lebanon, Israel, the Gulf microstates, Iraq, Afghanistan, Syria, Oman, Yemen and Saudi Arabia. It would abut against Central Asia at the Caspian Sea, and southern Asia at Pakistan.
"Central Asia." This would the places to the east of the Ural mountain, north of the Indian sub-continent, south of Russian Asia and west of China. (Turkmenistan, Uzbekistan, Kazakhstan, Tajikistan, Kyrgyzstan, Afghanistan and Iran)
" (North) East Asia". China, Mongolia, Eastern Siberia, Japan, Korea. If Mr. Putin continues to rely upon supplies, support and funds from China, we may well see the Kamchatka peninsula in eastern Siberia subject to historic claims by China. With a mere 140M Russians, I don't see how a distant Moscow regime could adequately maintain and defend a place larger than even Canada, most of which would be inhabitable, with an economy smaller than that of similarly-populated Mexico.