I note that your Pi-hole is configured for your Pi-hole host machine's eth0 interface, but that is connected via wlan0 instead:
*** [ DIAGNOSING ]: Network interfaces and addresses
2: eth0: <NO-CARRIER,BROADCAST,MULTICAST,UP> mtu 1500 qdisc pfifo_fast state DOWN group default qlen 1000
3: wlan0: <BROADCAST,MULTICAST,UP,LOWER_UP> mtu 1500 qdisc pfifo_fast state UP group default qlen 1000
inet 192.168.1.2/24 brd 192.168.1.255 scope global noprefixroute wlan0
valid_lft forever preferred_lft forever
inet6 240<redacted>d4/64 scope global mngtmpaddr noprefixroute
valid_lft forever preferred_lft forever
inet6 fe80::<redacted>18/64 scope link
valid_lft forever preferred_lft forever
That should not be an issue with your current Pi-hole Interface Settings (Allow only local requests), but still, you may want to run pihole -r with Reconfigure to adjust for wlan0 accordingly.
Your debug log also shows that you have defined some clients, all of them assigned to the default group, and you have only exactly one group, the default group.
This is a valid configuration, but you should note that Pi-hole would treat any client to the default group anyway, i.e. there would be no need to add clients if you intend to use the default group only.
As for your issue:
Pi-hole is not loading any websites - your client's browser does that.
Pi-hole can only be involved if it would not provide an IP address for a domain that a browser requests resolution of.
That could happen if your Pi-hole would block that domain, or if one of Pi-hole's upstreams would have issues resolving it (e.g. because it would be inaccessible, unresponsive or blocking domains itself).
If it is Pi-hole blocking some sites, How do I determine what domain an ad is coming from? may help you to find out which domains are involved.