According to $regex documentation:

MongoDB uses Perl compatible regular expressions (i.e. "PCRE" ) version 8.42 with UTF-8 support.

I believe this covers all server-side evaluation of regex patterns since the manual only discusses differing behavior related to Javascript ($regex vs. /pattern/ Syntax), which likely applies to the shell.

The current docs for MongoDB\BSON\Regex link to documentation for supported flags, but we'd do well to note the supported pattern syntax as well.