How could I generate a CRS field inside the GeoJSON object created by Leaflet layer.toGeoJSON?

You can just set the crs field:

object.crs =  {
  "type": "name",
  "properties": {
    "name": "epsg:3857"
    }
  }

Note however that the coordinates you give in your example really are epsg:4326 coordinates, which is also what leaflet would output by default. I don't think you need a change here.

I don't have enough rep to comment on the accepted answer.

This is a link to the comment made by @johanvdw saying the CRS for all GeoJSON is epsg:4326 (WGS84) https://tools.ietf.org/html/rfc7946#section-4