Welcome to the Cocoontech forum methos.
Electric is electric is electric.
There are no shortcuts.
Have a read here first:
How To: Replace a Light Switch
Basics have been mentioned above.
If you have any doubts about what you see or how to wire up an electric outlet or light switch I would personally call an electrician.
First and foremost when tinkering with your home electric is safety.
For the old fashioned analog light switch typically there are two wires; one being the line (black) and one being the load (goes to the lamp and can be black or some other color like red, blue or yellow).
Many automated switches are little computers and need neutral and ground these days.
Personally never seen or read about the Eufy Smarth Switch. Went to the website and they have no documentation posted for installation.
I looked on Amazon and there are pictures / reviews and really nothing about installation.
I did find a couple of pictures and drawings which show the switch to be wired to:
1 - neutral
2 - line
3 - load
4 - ground
Color defaults are typically
1 - white - neutral
2 - line - black
3 - load - can be yellow or blue or red or black depending on electrician - best way to check is at the light source wiring where you will see a white wire and another color going to the light bulb.
4 - ground - green - with metal conduit / pipes you can wire ground to box -
Romex I have seen and used is 3 wire plus ground wire (which is not covered).
Curious how many white wires are coming together there. Typically one white wire (neutral) goes back to the fuse panel and many times the neutral wire to a lamp goes through a switch box and many times it goes right to the light box.
You mentioned 3 wall gang box with two 3 way switches. A three way switch typically has two wires plus a traveler.
The three way switches each carry a load and line and traveler wire. I have seen the traveler wire be different colors.
The bundle of neutrals is rather large and thus far, unable to find ones of that size at the local box stores. Its already somewhat crowded in that box to add those mega wirenuts.
Break the bundle down to two bundles with an interconnect white wire. Typically the wire guage is 14. Maybe use a 12 guage white wire to interconnect the bundles.