It's already tagged as access=private, hence the fine dot pattern that appears on the standard map.

But this is also has a contradictory tag garden:type=community which means that it's "Located in parks or other public spaces" according to https://wiki.openstreetmap.org/wiki/Key:garden:type.

So, needs to wait for a passing editor to report on actual signage, gates and fencing before this can be resolved.