MacOS: curl (and rest of system) ignores a static DNS record (set on router) while nslookup shows it

I have a Seafile server running on a local network, and exposed to the internet (via port forwarding).

When I am outside of home, I can access the server just fine through the public hostname and port of my internet provider (eg. 123.myprovider.com:<my-port>), that forwards to my router (and that then forwards the specific port to a Seafile server), but I thought that when I am at home, the clients should know that the server can be reached at a local IP address (eg. 192.168.1.3) instead, so that they connect directly through LAN.

On my local DNS server (pihole) I have set up a static DNS record saying that 123.myprovider.com should resolve to 192.168.1.3.

And now the problem:

nslookup looks up the correct IP address all right:

> nslookup 123.myprovider.com

Server:     192.168.1.17 # this is my local DNS server - a pihole instance
Address:    192.168.1.17#53

Name:   123.myprovider.com
Address: 192.168.1.3 # this is exactly what should happen

However, curl (and all the other HTTP based tools, like browser) still report the public IP instead:

> curl https://123.myprovider.com:<my-port> -vvvv
*   Trying <my public IP address>:18275 ...

… and this fails.

I have flushed the DNS cache with sudo dscacheutil -flushcache; sudo killall -HUP mDNSResponder, but this doesn’t change anything.

Why does MacOS ignores the static DNS record from a local pihole, when nslookup uses it? How can I make it respect the local record?

Thanks for ideas!