Wiring – Installing a new smart switch into box, wanting to double check plan (primarily with regards to ground wires)

I'm looking to install a new smart switch into a 3 gang box. The current box has 3 toggle switches, each of which is without connection to a ground wire. The box itself has 5 sets of wires coming into the box, with all the grounds and neutrals bound together (either with wire nuts or with copper clamps). A picture of this is shown below (4 sets of wires coming from the top of the box and 1 set coming from the bottom that's harder to see):

The smart switch needs to be connected to neutral, and included with the smart switch is what appears to be a 12 AWG jumper wire for this purpose. My plan was to connect the load/lines as they were with the original switches, and then wire nut this 12 AWG wire with the other 5 (I think) 14 AWG neutral wires already in the existing wire nut with a new Ideal WT52-Red wire nut (which says on the box that it can handle 1 #12 with 5 #14s). Good so far, right?

My next question is how to do the grounding, and this is one that I'm more unsure of. The wires are there, as you can see. But I'll need to ground my new smart switch and will also want to ground the 2 other dumb switches that I'll be replacing simultaneously (since I want them all to be Decora style, and presumably new switches will have ground screws for me to take advantage of). What is the right way to do that grounding? Do I need to get 3 new 14 AWG copper wires to go from the ground screws to that bundle of ground wires there? If so, how should they be joined (that would be 8 #14s)? Would I have to crimp that together with a copper clamp or are there wire nuts that could handle that? I can't just have one of those existing ground wires (say, from each load) attach to the ground screw, right? That doesn't ground it?

Also, as a secondary question, why would there be 5 sets of wires coming into this box anyway? I would have figured that there would be 1 set from the line, and then 3 loads. I think these are all single-pole switches…

Thanks for any insight you can give.