You’re mixing together a few different concepts.

• Service dogs don’t need “4 skills.” They need to be trained to do at least one specific task to assist a person with a disability. Service dogs have public access rights (and housing rights) without their owners needing to provide any documentation.
• ESAs don’t have public access, but there are state and federal laws that pertain to housing and would allow a person with a disability to, for example, keep their ESA in an otherwise pet-free apartment. In those circumstances, the landlord can request a letter from the owner’s treating doctor that says there is a disability related need for the ESA.

Here’s the HUD guidance on service animals and ESAs under the Fair Housing Act, if you’re interested in more information: https://www.hud.gov/sites/dfiles/PA/documents/HUDAsstAnimalNC1-28-2020.pdf