The nut of the problem is the ground wire joining the neutrals in drawing 1. This is a bootlegged attempt to fix a fundamental problem of bringing 5 wires: 2 travelers, always-hot, neutral and ground in a /3+ground cable.
Everything in drawing 1 is bootlegging neutral from ground. This is bad and needs to be fixed Right Now. Not least, nothing in that box is actually grounded.
Good thing you're into smart switches
Because the real solution here is use smart switches to reduce the number of 3-way travelers, so we can free up the wire we need to do this right.
Theoretically, you can reduce the number of travelers from 2 to 0 with Insteon, X10 or other tech that uses powerline signaling to communicate between switches. However it will suffice to use smart switches that use 1 comms wire, so that is what I will describe.
- remove the 3-way from the 2-gang box. There, see the clump of blacks in the 2-gang box, which include a white from the /3 cable? Remove the white and replace it with the /3 cable's black (remove yellow tape). Now you have a 5-wire bundle of eevery black in the box (not blueblack) and a pigtail to each switch. These are always-hot.
- Notice the bundle of neutrals here. Add the /3 white wire to it, and also add a white pigtail that will go to the future 3-way smart switch. Now you have a 6-wire bundle (you will need a red or tan wire nut for that) with all white wires and a pigtail to each switch. These are all real neutral.
Remove the 3-way from the 3-gang box. There, see the /3 white going to a clump of black pigtails going on to switches? Remove the white and replace it with the /3 cable's black (remove yellow tape). Also add a black pigtail that will go to the future 3-way smart switch. Now you have all 4 uncolored blacks in a bundle (supply and 3 pigtails). These are always-hot.
Notice the bundle of neutrals here. Remove the /3‘s green wire and replace it with the /3’s white wire and add 1 white pigtail for the smart switches. Now you have 5 white wires (one from every cable plus the pigtail) so you'll need a red nut for this. This bundle is full; you'll add the smart switch pigtails to the other end of that white pigtail. All these white wires are neutral.
Now you have a loose ground wire. Joint it with every other ground in the box.
The red wire is now the only comms wire.
Whew!!! We have corrected the bootleg wiring, and have honest always-hot, neutral and safety ground in both boxes. The 3-way circuit is wrecked: cap off its wires until you procure a correct smart switch.
The 3-way smart switch "master" must go in the 3-gang box. It connects to line/always-hot (black), neutral (white), load/switched-hot (blue), and if needed, comms/traveler (yellow-red).
The 2-gang gets the 3-way smart "remote". It takes line/always-hot (black), neutral (white) and if needed comms/traveler (yellow-red).
The other smart switches install according to their instructions. The load/switched-hot wires all have colored tape on black.