OK, this was a confusing one for me. In the past, on macOS, when you clock on the Show Tabs Overview at the upper right of the Safari tab bar, I normally expect to see all the shared tabs from other devices. At least this is how it worked MacOS. It is now on the "Start Page" which is the default and you get all the tabs shared with you and also below that are the tabs open on other machines with a pull down on the upper right so they are grouped by machine.
The same thing happens on iOS, now if you want to see the shared tabs across devices, you do not click on the lower right icon which has what tabs are open. Instead, click on the plus sign on the lower left and get the same Start Page which has Favorites, tabs Shared with you from Messages and other places, and then way below the Privacy Report and your Reading List you will see a From section and the same pulldown.
So there are now many different paradigms for sharing things across devices and here is how I use them
- Group Tabs for Current Work in Process, when you click on the MacOS Show Sidebar, you will see them or on iOS if you click on the center button at the bottom you see these (and yes, the two systems have really different layouts). These are the semi-persistent tab groups that are great for researching things and quick context switchs. I have one group for "buy" that is things I'm trying to buy and "blog" for tabs that i want to blog as well as one for "dev" for active projects. You get the idea. I've definitely had problems syncing these and it requires that you toggle on and off iCloud sharing for Safari to make it work (on MacOS, go to System Preferences > Apple Id > Safari and on iOS goto Settings > Your Name > iCloud > Safari).
- Reading List for long web pages I want to read later quickly or put into Books for manuals and tutorials. If you have a web page that you want to read later *offline* then this is the place to stuff it. Tab groups do not work well on say an airplane. They do a refresh when you load them, but the Reading List works off line, just make sure on iOS this is set at Settings > Safari > Readling > Automatically Save Offline and in MacOS, it is Safari > Preferences > Advanced > Reading List > Save. To add a page to the reading list, in MacOS Safari, right click on the globe icon in the addres bar and you will get an option to save to Read. On iOS, click on the book icon that is second from the right and the center tab is a spectacle, this is your reading list and you open it, mark as read, so it is a nice queue of things to read later. You can also choose Edit to select delete the things. This Reading list is copied across all devices. If there are things that I know I want to keep for a long time like say a PyTorch Tutorial, you can also choose the Share button and Save as Book, this takes the page and turns into a PDF for reading later
- iCloud Tabs for current work I haven't stuffed into a Group Tab. These are tabs that aren't in groups and accessing them is a little different as mentioned above, you get them on the Start Page of Safari now. This is useful if you didn't have time to throw them into a group.
- Favorites for web actions and Bookmarks (almost never used). I actually almost never use these, but you can have static collections of links, this is useful if you are say a stock trader and you want to keep a list of all yours site. They can be favorites which stick in your favorites bar, you they can be Bookmarks (a Favorite is just a Bookmark Folder with a special meaning). I tend to use Favorites as a way to access things that are hard to get to or where there are actions like the WordPress PressThis action which blogs a particular page. I
- Shared with You for archiving links. These are all the links that someone has sent you via Messages, so its kind of like Reading List. These things kind of build up, so I usually ignore them, but I should really just remove them as they come in as they are still in Messages.