When I enter the ID string into the Connection ID box, I receive a message saying the Connection ID can't be more than 32 characters. What is happening here? Is the Connection ID somewhere else?
You want to be entering the string from the "ID" column, not the "UUID" column.
the connections are stored here - /etc/NetworkManager/system-connections/ - you can manually delete them from here...
That "Connection ID" field in Cockpit is likely pulling the SSID length limit (WiFi SSIDs max out at 32 bytes), not an arbitrary text field — so a long profile name will trip it even though NetworkManager itself doesn't enforce that limit. Easiest workaround: skip the GUI and use the terminal instead. Run nmcli connection show to list all profiles with their exact NAME and UUID, then delete with nmcli connection delete uuid (or nmcli connection delete id 'exact-name-here' if the name has spaces/special characters) — the UUID route avoids any length or matching issues entirely.