PureOS not able to connect to internet, accept through Tor Browser

right, so dns then. you can try to edit /etc/resolv.conf and set it manually to your dns name and resolver from dhcp, eg.

# echo "domain $(hostname -d)" > /etc/resolv.conf && dhcpcd -U wlp1s0|awk -F= '/domain_name_servers=/{print$2}'|tr " \047" "\012"|xargs -n1 echo nameserver >> /etc/resolv.conf

of course it may overwrite it on next nm event. Note # prompt - so as root. the command above extracts nameservers option from dhcp, but that could be disabled by dhcpcd config so you might need just to set nameservers manually with the editor to the right ip.