The links to your site section of Google Search Console is not very reliable. The links may all be there, and Google just isn't displaying them. When that happens Google still knows about them and is counting them towards your site's reputation.
From Google's help document about links to your site (emphasis added):
Not all links to your site may be listed. This is normal. In addition, Google has recently made improvements to how we gather and display link data (for example, link counts now include links redirected using 301 or 302 redirects). As a result, you may see a change in the number of links displayed for your site.
I'd recommend that you re-enable HTTPS for your site. When the option is available, there is no reason to keep using HTTP these days. When HTTPS is enabled, make sure you add your site to Google Search Console a second time with
https://. It is possible that your links would have just moved over to that profile in search console.