How exactly can I group booleans as one?

There are many ways that you could accomplish what you are trying to do.

You could just use an array:

 bool myBools[] = { false, false, false, false };
 
 void SetAll(bool b) {
    for(int i=0; i<myBools.Length; i++) {
       myBools[i] = b;
    }
 }

Or you could use a bitmask (note: I have never done this in C# or with Unity before). Check this out, though.

Edited to explain maps (in C# they are called Dictionary but in computer science in general, they are maps):

So in the above example we created an array of bools myBools but now we want to be able to give each one a specific name and reference it by that name.

For example, let's say we're creating a basic inventory system of fruit (see comments below). In this super-simple example, we'll just want to determine whether we even have any of a specific fruit.

We begin by creating a Dictionary which will map from a string to a bool because we want to be able to determine if we have a fruit knowing only its name.

Below is some example code showing how you could create a basic inventory system:

 using System;
 using System.Collections;
 using System.Collections.Generic;
 
 public class ExampleClass {
     //Declare our basic inventory
     Dictionary<string, bool> fruitInventory = new Dictionary<string, bool>();
     
     //A more advanced "how many do we have" inventory would be defined like this
     Dictionary<string, int> fruitQuantity;
     
     //We could also make a class for more advanced data
     public class FruitInventoryData {
         int numRotten;
         int numFresh;
         bool canMakeWine;
     }
     
     //And use a dictionary like this
     Dictionary<string, FruitInventoryData> fruitAdvancedData;
     
     public void ExecuteExample() {
         //Add some fruit to our basic inventory
         fruitInventory.Add("apples", true);
         fruitInventory.Add("bananas", false);
         
         //Can also access it like an array, but ONLY to change it.
         
         //This causes an error, because we have no data on mangoes yet
         //fruitInventory["mangoes"] = false;
         
         //But this does not, because we DO have data about bananas
         fruitInventory["bananas"] = true;
         
         //We can be safe like this - it doesn't get executed because we check if we have the key, first
         if(fruitInventory.ContainsKey("mangoes")) {
           fruitInventory["mangoes"] = false;
         } else {
           fruitInventory.Add("mangoes", false);
         }
         
         //And we can also easily iterate over dictionaries
         foreach(KeyValuePair<string, bool> fruitData in fruitInventory) {
             string fruit = fruitData.Key;
             bool haveThisFruit = fruitInventory[fruit];
             if(haveThisFruit) {
                 Console.Write("We have " + fruit + "\n");
             } else {
                 Console.Write("We DO NOT have " + fruit + "\n");
             }
         }    
     }

If you ran ExecuteExample you would get this output:

 We have apples                                                                                                                                                                                                                     
 We have bananas                                                                                                                                                                                                                    
 We DO NOT have mangoes   

And here is a link to this executing.