Hello! Astrophysicist here!
Really Long Stick into a black hole is an extremely fun game and let me tell you astrophysicists love to play mental games. Yes black holes do have heck of large gravity, but they don’t do much schlorping.
I’m going to assume several things here, the first of which is that by “into” the black hole we mean “past the event horizon” which is the point at which light cannot escape.
While in principle if you get close enough to poke at a black hole you should also be falling into it, I’m also assuming that we are far enough away and our stick is improbably long enough that I personally am not primarily under the influence of the black holes gravitational pull.
So in this situation your first and most immediate problem is that the force of gravity on your Black Hole Facing end of the RLS is going to be WAY stronger than the end that you’re holding onto, and so the stick will experience a stretching. Under most definitions of stick, stretch is not a thing they do very well, and so your stick will begin to fray, first by fracturing and then at an atomic level, into smaller and smaller pieces. If you’re poking a small (star sized) black hole this should happen well before you get to the event horizon. So small black holes will simply “nope” the stick before it can touch it.
Large black holes will nope the stick after they get into the black hole and so pulling this stick back out (good luck) will give you a shredded, slightly less Really Long stick.
If you want to nyoom your way around the black hole while you do this, you sure can, but you have a momentum problem with the twisting motion of the stick now and the easiest thing is to just smash the stick into the side of the black hole (this will also fracture the stick and then shred the fractured bits into finest powder).
Probably the most fun you can have with a black hole is, instead of Poke with Stick, throw some gas at it. Not only is gas something that can’t get shredded (it already has no structural integrity), you can watch it do the doomed coin spiral from a distance. AND. As the gas spirals in, it will heat up to a ridiculous temperature and start to glow with visible light. (and x rays. Free scan of every single bone you have. Medical or astrophysical doctors do not recommend standing nearby.)
If you’re lucky, you still get raspberry jam (plasma edition) because you can find the chemical compound responsible for the flavor of raspberries out in space, and if it was in your gas cloud, you now have superheated raspberry flavor that irradiates your bones.