I find that you need to configure all the ID mappings in /etc/pve/lxc/101.conf, like the way they do in the documentation, not just the 1000 idmap.
Here's my working setup.
Host: /etc/pve/lxc/112.conf
arch: amd64
cores: 1
features: nesting=1
hostname: alpine-3-15
memory: 512
mp0...