Having the footpath connected to the road there was technically correct, because someone walking on the footpath would be able to start walking on the road once the footpath ended.
You are right though that there isn't actually a path connecting them, so for more detailed mapping you can use the tags highway=footway and footway=link to connect the path and road, which is what I have just done. You can read more about that tag here: osm.wiki/Tag%3Afootway%3Dlink

Hi, thanks for contributing to OSM!
Just so you know, the name tag should only be used if something officially has a name. So frequently the name tag can be left blank. I've removed the name from the drop off road because I am guessing that is not the official name.

If the playground, field, and track do not have official names, those name tags can also be removed.

Here is an excerpt from the wiki which explains more:
"Do not construct names for features by combining the name of an enclosing feature with a description. For example, an unnamed fountain in XYZ Park should not be tagged with name=XYZ Park Fountain. Internal features to a named area should only be tagged with a name when they have a commonly-used local name, or some other indication (such as signage) of the feature's name." (osm.wiki/Editing_Standards_and_Conventions)