Since there wasn’t clear answer, I want to put my solution in here (also this topic is the first link when searching “timeshift do not create backup manjaro” so I think there must be some answer.)
Issue really was with this error:
[16:20:47] crontab -l
[16:20:47] Failed to read cron tab
By some reason my system (that I installed yesterday) didn’t start cronie service, so I enabled it via systemctl:
systemctl start cronie.service
And that worked for me!
Since I enabled boot snapshot, I rebooted PC, waited 10 minutes and snapshot was successfully created. Hope it will be helpful for someone.