Adding rivers to procedural generated 2D map

I'm using a noise function to procedurally generate a tile map, I was wondering if there is any way to extend what I'm already using to add the ability to create rivers to the map generation.

Currently I'm getting this:

And I'd like to find a method of doing this: Where large bodies of water are connected to one another as if they were a single continuous flow.

I have a Noise class that makes the values for the map.

 public class Noise {
 
     int seed;
     float frequency;
     float amplitude;
 
     float lacunarity;
     float persistance;
 
     int octaves;
 
     public Noise (int seed, float frequency, float amplitude, float lacunarity, float persistance, int octaves)
     {
         this.seed = seed;
         this.frequency = frequency;
         this.amplitude = amplitude;
         this.lacunarity = lacunarity;
         this.persistance = persistance;
         this.octaves = octaves;
     }
 
     public float[,] GetNoiseValues(int width, int height)
     {
         float[,] noiseValues = new float[width, height];
 
         float max = 0f;
         float min = float.MaxValue;
 
         for (int i = 0; i < width; i++) {
             for (int j = 0; j < height; j++) {
 
                 noiseValues [i, j] = 0f;
 
                 float tempA = amplitude;
                 float tempF = frequency;
 
                 for (int k = 0; k < octaves; k++) {
 
                     noiseValues [i, j] += Mathf.PerlinNoise ((i + seed) / (float)width * frequency, (j + seed) / (float)height * frequency) * amplitude;
                     frequency *= lacunarity;
                     amplitude *= persistance;
                 }
 
                 amplitude = tempA;
                 frequency = tempF;
 
                 if (noiseValues [i, j] > max)
                     max = noiseValues [i, j];
 
                 if (noiseValues [i, j] < min)
                     min = noiseValues [i, j];
             }
         }
         for (int i = 0; i < width; i++) {
             for (int j = 0; j < height; j++) {
 
                 noiseValues [i, j] = Mathf.InverseLerp (max, min, noiseValues [i, j]);
 
             }
         }
         return noiseValues;
     }
 }

And in my main class the map is created with the following function:

 float[,] noiseValues = noise.GetNoiseValues (width, height);
 
         for (int x = 0; x < Width; x++) {
             for (int y = 0; y < Height; y++) {
                 tiles[x,y] = new Tile(x, y);
                 if (noiseValues[x,y]  < 0.2f) {
                     tiles [x, y].Type = TileType.Shallow;
                 } else if (noiseValues[x,y]  < 0.4f) {
                     tiles [x, y].Type = TileType.Grass;
                 } else if (noiseValues[x,y]  < 0.55f) {
                     tiles [x, y].Type = TileType.Scrub;
                 } else if (noiseValues[x,y]  < 0.6f) {
                     tiles [x, y].Type = TileType.Marsh;
                 } else if (noiseValues[x,y] < 1f) {
                     tiles [x, y].Type = TileType.Bare;
                 }
             }
         }

I'm very new to Unity and C#, I've done some reading around generating biomes but the math is somewhat above my head. Is it possible to extend what I have to accomplish river generating? Or could I use something like PathA* to join two points on a map to get the result I want? Thanks!