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There are a large number of missing backlinks (old) which are not showing on Moz but do show on Ahrefs. Is there a reason for this? Thanks.

We had a site redesign launch a few months ago. Due to other priorities / a lot of things going on, there were a decent amount of URLs that 404ed. We implemented a drupal module search404 to redirect all of these to the homepage or a search results page that pulls search terms from the 404 page. Our goal is to recoup SEO value since we saw a notable dip in domain authority and amount of links after launch. We know a catch-all automated solution like this isn't ideal because it's better to 301 each page to its most relevant live page. For example, if CNN.com links to our Texas location, it's better to 301 to our new texas page than a homepage or search page. The problem is that since we implemented this catch all search404 module, it seems like tools like Moz Pro and Screaming Frog are not picking up the backlinks from external sites that 404 since they were "fixed" by the search404 module. Any ideas on solutions? We're trying to avoid tedious or risky solutions like undoing the module, which may bring back the 404s but cause some UX and SEO issues so we can run a SF crawl. Or going through every link in our link profile manually to check.