Is this a lab / home network or a production network? Is the issue that all traffic passing from AnyConnect through the ASA not passing? or is it specific traffic?
I suggest breaking this up into two parts. First troubleshoot the issue with access to the internal server, and then troubleshoot access to the internet via tunnel all.
First off for testing with ping we need to enable inspect icmp in policy-map
policy-map global_policy
class inspection_default
inspect icmp
First verify the server reachability by pinging 172.16.10.10 from the ASA CLI.
setup a capture on the inside interface:
cap capin interface INSIDE-1 match ip 10.1.1.0 255.255.255.0 host 172.16.10.10
Now connect to the VPN. First check the Route Details in the AnyConnect client and make sure that secured routes is 0.0.0.0/0
Send some ping packets and then issue the command "show cap capin" and check if you are seeing traffic leaving the inside interface.
If you are seeing traffic leave the interface but get nothing in return, then there is an issue between the ASA and the 172.16.10.10 server.
If you do not have an internal DNS server that can resolve the URL or FQDN to an IP then you will need to access that server via IP.
Post the results from the tests here please.
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