Perfect that did it (No changes to HA Hassio just works after this change)
Synology NAS are the perfect companion to running Home Assistant. But by default, the DSM Reverse Proxy does not configure its NGINX settings to allow WebSocket, and some extra configuration will be required to get the Home Assistant frontend working with the DSM.
TEMPLATE CHANGE
To allow WebSocket by default for all service exposed by NGINX, you can enable it in the template file located in /usr/syno/share/nginx/Portal.mustache. Please be really careful in editing this file since you may break access to the DSM UI. Please backup this file before any edition.
Open /usr/syno/share/nginx/Portal.mustache and add the followings in the Location section:
proxy_set_header Upgrade $http_upgrade;
proxy_set_header Connection "upgrade";
proxy_read_timeout 86400;
Then restart the NGINX daemon:
sudo synoservicecfg --restart nginx
ONE THING: I would still like to know if I could make some kind of redirect for all HTTP to HTTPS on the HA
So any access to the a HTTP://IP:PORT is redirected to the new default working HTTPS://DOMAIN.COM
That part is still not working (Only port open is 8123)