The Lightsaber parasol is not itself a lightsaber, it is a Lightsaber auxiliary. It does not generate its own blades but redirects and splits the inserted lightsaber's blade. Based on this info I am guessing the Farkiller of Oo'ob the Apostate or the Lightsaber Rifle would be the Jedi versions of such technology.

https://starwars.fandom.com/wiki/Parasol_auxiliary

https://starwars.fandom.com/wiki/Lightsaber_auxiliary

According to Wookieepedia (which I use as the main source for my stats).

"The lightsaber parasol was a Sith lightsaber created by Kouru, a female Sith who led a bandit group. It functioned as a singled-bladed lightsaber when she used only the lightsaber hilt. With its attached parasol auxiliary, it produced multiple red plasma blades in a manner that resembled a parasol, particularly when she spun it to create a shield."

So it is a lightsaber, and it is an auxiliary. So you're right, but so is the above :)