A quick browse of some Russian forums (ixbt, rsdn) shows a significant, loud support for the official Russian govt line. Subjectively, how does it look to you? Do your coworkers, neighbours, relatives appear to be supporting the war?
Edit: I checked the petition text[0] and it says not 'war' but 'special military operation'. If they wrote 'war', obviously Putler could have said "there is no war, so wontfix".
[0] https://docs.google.com/forms/d/e/1FAIpQLScEsxsoXl_7R4aD5F8-...