A 301 redirect entails moving from one URL to another, be it a http to https for the same domain or from one domain to another.
When a link is reported as "lost" from the "old" page due to a 301 redirect and another link is still present on a "new" page, this other link will soon be added back to the Ahrefs backlink profile as a "new" link.
These changes might not be instantly visible in Ahrefs due to the way our Ahrefs' bot works. The fact that the bot has discovered a redirect of an old page doesn't mean it will crawl the new one immediately. The crawling is scheduled for sure, but it just takes a little longer.
To give you an example, when Ahrefs blog underwent a 301 redirect by moving from blog.ahrefs.com to ahrefs.com/blog, a site that we linked to ie. quicksprout.com received a "301 redirected" reason within their "lost backlinks" report for the link from blog.ahrefs.com that was "lost". There was certainly a "new" link from ahrefs.com/blog linking back to quicksprout.com but it took a while before this "new" link was added back to the quicksprout.com's backlink profile.