I’ve encountered this for new GTM installations to sites (first time GTM is being implemented or new container-ID being added).
Tag assistant looks like it is taking a very long time to connect or not connecting at all. This prevents you from entering preview mode.
First, check that the container-ID (GTM-XXXX) you’re adding is the correct one and the code snippet is in the right place.
If you have never published a container before on the site, then click Submit to publish the container.
Publishing this new container for the first time should fix the issue of tag assistant not being able to connect / not being able to go into preview mode.
If preview mode was working fine before and suddenly stopped working/tag assistant cannot connect, try selecting / deselect variables then publishing the container with these minimal changes.