Discovery, who owns Discovery, Food Network, Cooking Channel, and HGTV, to name a few, isn't moving to subscription. They already started Discovery+ which has most of the current & former shows on the networks, plus some exclusive shows from Magnolia, but doesn't have 'Live TV' for any of the networks, and not all seasons of some shows currently airing, are available on Discovery+.
The 'TVE' sites are the sites that allow cable, satellite, and streaming services to allow 'Video on Demand' viewing, and are current with all seasons. These ''Go' sites also allow you to watch each channels 'Live TV' as well as giving you access to their current 'On Demand' libraries. A valid login to a cable, satellite, or streaming service is needed to gain access. I use Fire TV, and there are individual apps for the channels I watch, and each gives me access to 'Live TV' for that channel, and access to the 'On Demand' libraries for the others. The exception to this is the Magnolia app.
The Magnolia Network is the new network started by Joanna & Chip Gaines and combined with the old DIY network to get them back to TV. They have their own site (Magnolia.com) that you can log into using your 'Discovery+' credentials. You can see the list of 'On Demand' shows for their network as well as the old DIY network, but they don't have the option to watch 'Live TV'. Fire TV has the 'Magnolia' app, but it just takes you to the Magnolia.com site which doesn't have an option to watch 'Live TV'
The only way I've found to access 'Live TV' for the Magnolia Network is from 'https://go.discovery.com/channel/magnolia-network-preview-atve-us or https://watch.hgtv.com/channel/magnolia-network-preview-atve-us' sites using valid credentials.