Ok, those are an unusual bunch of colors. If it's a "factory built" bike, that probably isn't suprising. Perhaps that makes it difficult to follow the wires and see what they go to.
You could do more research by looking at the wiring codes that most controllers have on their "vendor" page to see if you see one that matches. But I doubt you will.
What I would do is get one or two new controllers (they are cheap and a spare is always good), ID the wires needed to make it run (Which I will do below) and go from there.
But first, you need to think of what features does the bike have and how bad do you want to keep them. Does it have a display, what type? Does it have PAS? Does it have a speed-limiting switch, how many speeds? On/Off switch?
In general, we know;
1)Big red and blk - power
2)all reds - positive ( switched only by the main switch)
3) all blk.s and gr.s - Neg.
4) Blu - often a "trigger" to turn the system on.
5)Big red, blk, Yel, Blu and Gr - phase
6)Tiny of the same set - Halls
7)Sm. red/ Gr/ Blk - throttle (These may vary by one color)
Unless there is bundle that goes to a display, that's usually what it takes to make the bike run.
PAS wires look like throttle wires and both will have 5 Volts across the Pos./Neg. w/ the remaining wire the "signal" (varies 1 to 4 Volts depending on device position)
The good news is, beside crossing the Pos and Neg. wires (especially the big ones), you can't hurt the controller by connecting the other wires incorrectly. It just won't work.
In answer to your question those wires you mentioned are probably for the Brk. cut-off circuit and split to facilitate going to both brk levers. Or they are for something called EABS, which nobody here has ever figured out what that is.
When trying things out, leave grouped wires that you are unsure of dis-connected and they are out of the loop.
I always get my controllers from this out-fit;
https://www.ebay.com/str/diyebikestore/Controller/_i.html?_storecat=3549975010
I don't know if they are any better than the others (if they work, they are pretty much all the same), but I do know some of what's sold is junk.
This ebay store is actually PWS Power, a big vendor out of Singapore and they are prompt and their products are good.
When trying everything out, you can use wire-nuts for temp. connections and we can go over more perm. ones if you get that far.
I would get the 350W over the 250W, although it will pull a littler more from your batt., it will add a little more "torque".
If your batt is original and more than a year old, it could be that when you get everything working, it will start dying.
That's the way ebikes work (or don't

.