Your last output shows this configuration file that is causing unbound to be a forwarding resolver, not a recursive resolver:
/etc/unbound/unbound.conf.d/resolvconf_resolvers.conf:forward-zone:
/etc/unbound/unbound.conf.d/resolvconf_resolvers.conf: name: "."
/etc/unbound/unbound.conf.d/resolvconf_resolvers.conf: forward-addr: 1.1.1.1
/etc/unbound/unbound.conf.d/resolvconf_resolvers.conf: forward-addr: 1.0.0.1
This is caused by resolvconf running in the current (October 2021) Raspberry Pi release of the native Bullseye image.
If you check in file /etc/resolvconf.conf, you will see this as the last line.
# Configuration for resolvconf(8)
# See resolvconf.conf(5) for details
resolv_conf=/etc/resolv.conf
# If you run a local name server, you should uncomment the below line and
# configure your subscribers configuration files below.
#name_servers=127.0.0.1
# Mirror the Debian package defaults for the below resolvers
# so that resolvconf integrates seemlessly.
dnsmasq_resolv=/var/run/dnsmasq/resolv.conf
pdnsd_conf=/etc/pdnsd.conf
unbound_conf=/etc/unbound/unbound.conf.d/resolvconf_resolvers.conf
Comment out that last line.
Then, remove the configuration file that Raspbian put into your unbound configuration folder:
sudo rm /etc/unbound/unbound.conf.d/resolvconf_resolvers.conf
Then restart unbound
sudo service unbound restart
and unbound will be back in recursive mode.