Nginx websocket reverse proxy remove location

Question

Trying to set up an nginx https reverse proxy to home assistant, this works:

...
location / {
        proxy_pass http://127.0.0.1:8123;
        proxy_redirect http:// https://;
        proxy_http_version 1.1;
        proxy_set_header Upgrade $http_upgrade;
        proxy_set_header Connection $connection_upgrade;
}

But I would like to access it from a non-root url like home.local/ha. Similar to the goals of this question's asker. I have tried all of the answers on that thread, but none seem to allow the websockets to connect (I think). An example of something I tried:

...
location = /ha {
        return 302 /ha/;
}

location /ha/ {
        proxy_pass http://127.0.0.1:8123/;
        #proxy_redirect http:// https://;
        proxy_http_version 1.1;
        proxy_set_header Upgrade $http_upgrade;
        proxy_set_header Connection $connection_upgrade;
}

Any Ideas how I can get this to work?