The ESRIJSON driver that is responsible for FeatureServer does not support handling multiple layers at the same time, you have to query layer per layer.

For example:

    ogr2ogr -skipfailures  -f  GPKG floridaData.gpkg "https://services.arcgis.com/V6ZHFr6zdgNZuVG0/ArcGIS/rest/services/COVID19Surge_Florida_InterventionScenarios/FeatureServer/0/query?where=OBJECTID+%3C1000&geometryType=esriGeometryEnvelope&spatialRel=esriSpatialRelIntersects&outSR=4362&returnGeometry=true&sqlFormat=standard&f=json&maxRecordCountFactor=30&outFields=*&returnExceededLimitFeatures=false&resultType=tile" -nln 0
    ogr2ogr -skipfailures -update floridaData.gpkg "https://services.arcgis.com/V6ZHFr6zdgNZuVG0/ArcGIS/rest/services/COVID19Surge_Florida_InterventionScenarios/FeatureServer/1/query?where=OBJECTID+%3C1000&geometryType=esriGeometryEnvelope&spatialRel=esriSpatialRelIntersects&outSR=4362&returnGeometry=true&sqlFormat=standard&f=json&maxRecordCountFactor=30&outFields=*&returnExceededLimitFeatures=false&resultType=tile" -nln 1

[For more info][1]


  [1]: https://github.com/OSGeo/gdal/issues/4613#issuecomment-937529710