I don't know russian and can't read most of that anyways. Here's for polish: https://en.wiktionary.org/wiki/kobieta and it's definitely mare in croatian, and via that same in all languages in the region since we share large volume of vocabulary.
You should check in a real etymological dictionary. It's not entirely clear what the origins of 'kobieta' are whereas those of 'mare' are fairly well understood - it helps that it's practically universal in all slavic languages. There are lots of etymological mysteries out there, even surrounding very common words. It's fun to try but they generally don't get resolved by thinking of a somewhat similar-sounding word in a related language and glancing at wiktionary.