It is indeed a word.
It means exactly the same as "thus", and is thus (see what I did there!) superflous in most people's view, as the -ly adds nothing to what is already an adverb.
To many, such as your good self, it does sound awful, but not to me.
When I use it, which isn't often at all, it tends to be in place of "as such" (i.e. when referring to something already explained), especially when ending a sentence with it.
I.e. I could have said, and probably more often do say, "Some versions of the Bible, at least online, still refer to him
as such."
I could also have just use "thus" but, to me, there feels like there's then an expectation of stating what that "thus" is.
As in "argument, argument, thus conclusion".
To me, "thusly" suggests that the detail of the conclusion being referred to has already been stated.
That's just the way I use it, at least.
But I wouldn't say I use it regularly.