Help identifying this rope.

Do you have the slightest idea of where this “info” originates
(or echoes from) ?! You have no idea …, and neither do I, who
has done searching through many known sources (ABoK,
Hensel & Gretel’s EKFRW, CLDay’s AKS & Sailors’ Knots,
Svensson’s Handbook of Seaman’s Knots, George Biddlecomb’s
The Art of Rigging, and --now viewable HERE, in Books (pdf)–
Admiralty Manual of Seamanship & Aldridge’s echo of that
(seemingly). All point to gangway assists.
Some curiosities arise :: two sources say that the man-rope
knot should NOT be used qua stopper (but then what’s it do?),
and your image suggests --as does an Ashley note-- that the
manrope-knot’d end will see wear/loading!?

A man‑rope (sometimes just called a “man rope”)

Ah, so sometimes one calls it without the hyphen! Good one.

The knot can be tied and untied rapidly

?! The man-rope knot is a multi-strand end knot;
it is not tied & untied all so quickly.

Tighten the knot by pulling both ends; the result is a compact, secure hitch that can be released with a quick pull on the working end

Utter rubbish!

they can wrap the man‑rope around a belaying pin and tie a simple knot (often a man‑rope hitch ).

  1. Tie a man‑rope hitch around the belaying pin, then loop the sheet through the same hitch.

Good luck learning what that “man-rope hitch” is :: Google
finds it in one place only --this thread! Really, nearly all of
what’s seen here has spit out by AI is rubbish.

it became a staple of everyday seamanship,

Yep, sure did --one can read about it alllll over.
Just go down to a sea port pub and ask any ol’ sailor
"Old salt, how to you knot your man rope?! "
You might get better responses than from AI!

(-;