For that, you might as well just use the regex functionality in man itself too. But that misses the point.

The goal of grepping in that snippet is that you're `less `ing through precisely the parts that matter, and no more, rather than wading through the whole man page, and you're using -C to control how much context you (think you) need around the search results. This is a much better setup for skimming through potential hits than going through the man page wall of text.

'man' has no regex functionality; on most Unix systems, it just uses 'less' as its pager.

IIRC you don't need to pipe to less at all for that - man already supports it. grep -C gives a good summary of the various options, then you can just pull up the man page and use that selfsame search to get details that might've been cut off.

You can also do that directly in 'man'.

No. All three of the responders so far have implied that this functionality is in man. It is not. It's in the pager that man invokes; ironically often, but not necessarily always, that very same less program.