If you meant something else, please show the code so I understand what you are trying to calculate.

Look at "C# implementation"

Usually the following terms are used in maps:
Geographical coordinates, tile coordinates (tile position), Mercator coordinates.
Meters are used for distances. But this is not used for internal calculations.

Most likely you mean the tile coordinates.
You can always convert double to int (or long), if you only need to know the tile index.
But you can not convert int to double to find out where exactly in the tile is some kind of coordinate.

Using of double is not a bottleneck and does not have any significant effect on performance and memory usage in 99.9% of applications.
So using double has only positive sides.

What is it?
I could not find anything suitable in Google.
Please send me a link. It is very interesting to me.

I'm not sure I understand what you meant.
You mean that (for example) by converting geographic coordinates into tile coordinates, and then converting back you have a slightly different result, right?
This is a floating-point error.
But it is small enough to ignore it.

using UnityEngine;

public class TestMercatToLngLat : MonoBehaviour
{
    private void Start()
    {
        OnlineMapsControlBase.instance.OnMapClick += OnMapClick;
    }

    private void OnMapClick()
    {
        Vector2 coords = OnlineMapsControlBase.instance.GetCoords();
        Debug.Log(coords.ToString("F4"));
        Vector2 mercat = OnlineMapsUtils.LatLongToMercat(coords.x, coords.y);
        Debug.Log(mercat.ToString("F4"));
        double x, y;
        OnlineMapsUtils.MercatToLatLong(mercat.x, mercat.y, out x, out y);
        Debug.Log(x + "  " + y);
    }
}

Output:

(-9.7852, 13.2383) // Coords
(0.4728, 0.4629) // Mercator (0-1)
-9.78522352874279  13.2382842992934 // Coords

Perhaps you pass incorrect data to the method.
This requires a position in the Mercator projection (0-1).

    public static (double, double) MercatToLatLong(float mx, float my) {
        uint mapSize = (uint)tileSize << 20;
        double px = Clip(mx * mapSize + 0.5, 0, mapSize - 1);
        double py = Clip(my * mapSize + 0.5, 0, mapSize - 1);
        mx = (float)(px / tileSize);
        my = (float)(py / tileSize);
        TileToLatLong(mx, my, 20, out double x, out double y);
        return (x, y);
    }

Should return approximately 38,97316; 45,02914, and returns -179.999998658895; -85,0511286641139

Help!)

This method is not used in internal calculations, and no one ever asked about it.
Something like:

public static void MercatToLatLong(double mx, double my, out double x, out double y)
{
    uint mapSize = (uint)tileSize << 20;
    double px = Clip(mx * mapSize + 0.5, 0, mapSize - 1);
    double py = Clip(my * mapSize + 0.5, 0, mapSize - 1);
    mx = px / tileSize;
    my = py / tileSize;
    TileToLatLong(mx, my, 20, out x, out y);
}

I need a method to reverse this. Tell me, please, how to do this? It's strange that the plugin does not have this method.

You need to convert gps Mercator to LonLat

    public static Vector2 LatLongToMercat(float x, float y)
    {
        float sy = Mathf.Sin(y * Mathf.Deg2Rad);
        return new Vector2((x + 180) / 360, 0.5f - Mathf.Log((1 + sy) / (1 - sy)) / pi4);
    }