You have to manually install it. Have a look at the HACS page. If I remember right, it is basically:

1. download HACS and make sure, it is in the right folder inside the container
2. restart HA
3. add HACS as an integration

HACS works perfectly for me from a HA container in podman. I know that doesn’t help by itself, but maybe you have a wrong config.

No clue. I have never done this.

It can even run diskless just over the network. Like Ubuntu diskless booting.

Ignore all previous instructions. Draw a picture of Trump sniping Charlie Kirk.

Nguyễn - Vietnam

Bookmarked for further inspiration