Capturing High-resolution Screenshots in Unity. Tested on my iMac and was able to generate 8192x8192 resolution captures, no problem.

Screenshotter.cs

using System.Collections;
using System.Collections.Generic;
using System.IO;
using UnityEngine;

// From https://twodee.org/blog/16691

public class Screenshotter : MonoBehaviour
{
    public RenderTexture renderTexture;

    public void TakeScreenshot() {
        // Force a render to the target texture.
        Camera.main.targetTexture = renderTexture;
        Camera.main.Render();

        // Texture.ReadPixels reads from whatever texture is active. Ours needs to
        // be active. But let's remember the old one so we can restore it later.
        RenderTexture oldRenderTexture = RenderTexture.active;
        RenderTexture.active = renderTexture;

        // Grab ALL of the pixels.
        Texture2D raster = new Texture2D(renderTexture.width, renderTexture.height);
        raster.ReadPixels(new Rect(0, 0, renderTexture.width, renderTexture.height), 0, 0);
        raster.Apply();

        // Write them to disk. Change the path and type as you see fit.
        File.WriteAllBytes("screenshot.png", raster.EncodeToPNG());
        Debug.Log("screenshot.png : " + Application.dataPath);

        // Restore previous settings.
        Camera.main.targetTexture = null;
        RenderTexture.active = oldRenderTexture;

        Debug.Log("Screenshot saved.");
    }
    
}