[SOLVED] How can I get the local domain name auto suffixed to hostnames in DHCP?

You have a couple of options here.

By default, Pi-hole's embdedded dnsmasq would only automatically add DNS records for a simple hostname expanded by the local search domain if a DHCP client would claim that hostname during DHCP lease negotiation.
If I remember correctly, this also would mean that the lease had to be active, but you want to verify that.

As you've observed, any manual DNS definitions (including CNAMEs, PTRs, SRVs, etc.) would be added as is, i.e without considering the search domain.

You may try to enable expand-hosts as a custom configuration option, but note that according to dnsmasq documentation , this won't work for all definition types, but for definitions in hosts files only.

For configurations where Pi-hole is acting as DHCP server, ticking Never forward non-FQDNs would also prompt an expand-hosts option to be set.

Adding the DNS records explicitly may be more tedious, but it certainly is the safer way to provide resolution for local FQDNs, and it will also work when Pi-hole is not your DHCP server.