I had the same problem. In the log I could see the error:
[Apr 7, 2022, 14:00:37] Unknown pushed DHCP option: [dhcp-option] [DOMAIN-SEARCH] [your.domain]
The solution is to add the following option to your openvpn server (PfSense): push "dhcp-option ADAPTER_DOMAIN_SUFFIX your.domain"
After connecting you can see in the log (verb 4) that adapter_domain_suffix is now set
[Apr 9, 2022, 02:40:01] SetupClient: transmitting tun setup list to \\.\pipe\agent_ovpnconnect
{
...
"tun" :
{
"adapter_domain_suffix" : "your.domain",
"block_ipv6" : true,
...
And now local names are automatically resolved to FQDN:
C:\>ping xbuilder
Pinging xbuilder.your.domain [192.168.41.7] with 32 bytes of data:
Tested with OpenVPN Connect 3.3.6