192.168.3.1.53: UDP, length 39
So that is your client at 192.168.3.3 asking for dns.. Pfsense does not answer - so no how would the client go to any website? if can not look it up. So looks you do not have unbound running or forwarder working at all.
Or you don't have any firewall rules on this interface to allow access? The lan interface would have a default any any rule on it. Some new interface you created would not have any rules you would have to put either an any any or the rules you would like to allow.
Pfsense will create behind the scene firewall rules to allow for dhcp to work.. But I only see this
23:37:25.457114 IP 0.0.0.0.68 > 255.255.255.255.67: UDP, length 300
23:37:25.457435 IP 192.168.3.1.67 > 192.168.3.3.68: UDP, length 300
there should be more.. from what have to assume is the discover there to FF:67, the answer would be a offer - but you should then see a request and ack..
But clearly from this whatever .3 is sending traffic to .1 (pfsense).. I take it .3 is a wifi client? So where are the rules on this interface on pfsense?