Verify All Domain Variations in Search Console
In Webmaster Tools, you need to verify all combinations of your domain. e.g. www/non-www, http/https in order to see all the backlinks.
Redirecting URLs Do Lose Some PageRank
Changing URLs and using redirects does result in a small loss of PageRank. Keeping original URLs is still better if possible. This is also why Google recommend updating backlinks.
Backlink Data in Search Console Is Delayed
Backlinks reported in Webmaster Tools come directly from the Googebot web crawling process, give or take a few days delay.