How to connect a neutral wire to a bundle?
Easy.  You have five cables coming into the box

supply from upstream
onward supply to other downstream loads.
switched load to device 1
switched load to device 2
switches load to device 3

Each load line has a switched hot and a neutral.  I would mark the switched hots with colored tape, red, blue, yellow etc.
The switches each connect to an always-hot and a switched-hot. Sometimes installers do clever things to daisy-chain the switches, so there aren't 3 always-hots coming from the switches.
So I would expect 5 always-hots nutted together: supply, onward, and 3 switches.
And 5 neutrals nutted together: supply, onward, and 3 loads.
And of course each switch nutted to a switched-hot, if they have pigtails and are not connected directly.
Now with 3 smart switches, you'll have as many as 8 neutrals.  That's too much for a wire nut, especially since smart switches tend to have pigtailed wires smaller than the other wires.
I would get a 6&quot; length of white wire (only white or gray will do) and make a pigtail fo break up that fat wire nut, e.g. Put both supplies, the pigtail, and a couple loads under one large wire nut, then put the other end of the pigtail, remaining loads, and smart switches under another wire nut.
If the wire nuts are &gt;10 years old, replace them.  The new ones are much better.