Google does not show all links, and not all spammy links, within the Search Console links report. This is not new, Google has long said that the link report only shows a sampling of links. In fact, Google even shows disavowed links in the link report.
John Mueller from Google recently responded to a question about this on Reddit where the SEO was concerned about his site accumulating spammy links daily and while Semrush reports show the spammy links, Search Console does not. He asked if he should care.
John Mueller replied, "I wouldn't anchor on whether Search Console shows them, but if these are random spammy links on the web, I'd just ignore them."
Here is that thread:
This means that just because Search Console does not show the spammy links, it doesn't mean that they are not known by Google. But he also said, if they are random spammy links, you can ignore them - which is the advice Google has given for a long time now. In fact, Google said they do not notify sites of spammy links because Google ignores those links. As a reminder, since Penguin 4.0 update Google devalues bad links versus demoting the pages they link to.
John Mueller in general is not a fan of toxic link reporting. In fact, Google has many many times told SEOs to not use the disavow link tool. Saying many times not to disavow, that it hurts more than helps in some cases. Google even blasted some agencies selling disavow services. Not too long ago, Google also said to ignore toxic link reports, also saying disavowing based on third-party metrics is not a good idea.
Forum discussion at Reddit.
