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.
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.)