I can access the ESP-01 WiFi board at it’s own local IP address, but I’m having issues connecting to it over my local WiFi (http[s]://yourelegoo.local and/or local WiFi IP address.
This can be caused due to several reasons.
Any connection issues related to the http[s]://yourelegoo.local is usually caused by mDNS (MultiCast DNS) not working properly on your local WiFi router or due to a local firewall. Here are some pointers you might want to consider:
Local WiFi network needs to be set to public (not private).
For Windows OS, try going in to "Firewall & network protection" -> Advanced settings -> inbound rules and make sure all 3 mDNS entries are enabled, likewise for outbound rules.
For Windows OS, Check this registry key: Computer\\HKEY_LOCAL_MACHINE\\SOFTWARE\\Policies\\Microsoft\\Windows NT\\DNSClient\\EnableMulticast.
Turn off all external firewalls, such as AVG (you may want to re-enable your firewall when not using the Elegoo car for safety).
For Windows OS, uninstall Apple Bonjour Service.
Removing IPv6 from the wireless network adapter if your router is set up with only IPv4.
Turn DNS Filtering off on your router for the Elegoo IP.
The main reason why the “programmer not responding” happens is that the socket can't be opened (another program is connected to the ESP-01 or mDNS name lookup failure are the top reasons).