Comprehensive guide to linking domain purchased from NameCheap to NCP

Nextcloud version (eg, 10.0.2): NextCloudPi v0.41.7
Operating system and version (eg, Ubuntu 16.04): Raspbian Lite
Apache or nginx version (eg, Apache 2.4.25): Apache2.4.25-3+deb9u3
PHP version (eg, 5.6):7.0.19-1

The issue you are facing:
I have bought a domain on NameCheap and have configured my A records to the following.
A record @ Automatic
A record www Automatic
A record * Automatic

I have set up portforwarding on my router for port 80 and 443 using NCP’s portforwarding configuration, tested postitive on, and disabled uPnP afterwards. My pi has a static IP connected via ethernet to the router, yet Let’s Encrypt detects no internet connection. SInce I have a domain and a static IP, I am not sure the DDNS suggestions would be what I need. I am able to log into the config page, but unable to change the default password.

Your pi has a static local ip. But do you have a static public IP as well? Then you can directly put it into the DNS settings. If your public IP can change, I would use a dynamic DNS service and then put a cname-record to the DNS of your Domain linking to the dynamic DNS name.

Keep in mind that if you change DNS entries, normal DNS servers cache entries for quite some time and changing IPs can take up to 24h to propagate to all DNS resolvers.