I suspect, without having researched it, that människa and mensch are direct cognates where vowels have been inserted for various reasons.

It's not unusual that an affix can have a form with a vowel that gets lost or added, or that cognates can have different morphemes in addition to their shared morphemes. (For the latter case, when writing about Grimm's Law above, I re-learned that although "hundred" is cognate with "centum", the "red" part is a separate Germanic morpheme meaning 'count'. For that matter, the "um" part is a separate Latin morpheme that is a neuter noun ending.)

Mensch, människa, menneske, ..., and (most likely) manusha are cognates. But it's still curious how "manusha" sounds like "människa" while the vowels have been dropped in "mensch".

For some reason German sometimes drops the i in "-isch" (cognate with English "-ish"). But the only reasonably common examples I can think of are Deutsch (etymologically definitely with -isch/-isk) and Kölsch ('pertaining to Cologne'). I don't know if this is somehow an example of a more widespread phonological process in German.

In Swedish, "isk" endings are sometimes contracted to "sk" such as "polsk"="polish" and the only way to say "pertaining to Köln" would be "kölsk" (unless specifically the beer.)

But "människa" is a noun. It's pronounced "menisha" but it doesn't mean "manish". In Norwegian, the word for humane is spelled "menneskelig" literally "menneske-like". (In Norwegian the 'k' is hard.)

As I can gather, the literal meaning in sanskrit of "manusha" = "born of Manu" = human. Manu is a god.

Wiktionary claims that "människa" does mean "manish" (and that it's a direct cognate with "mensch"):

https://en.wiktionary.org/wiki/Reconstruction:Proto-Germanic...

It's just that that etymology has become opaque to modern-day Germanic language speakers.