In former versions of Toolset Views, it was possible to define a custom search view by placing the search form and the result loop on DIFFERENT pages (especially to avoid to have a listing of all objects on the search page before the filter is used.) I can't find this funcionality anymore in the Blocks version. Has it been dropped, or is still possible, and if yes how?
This hasn't been added to Blocks yet, it is on the roadmap along with some other features that are still only possible with the classic editor for Views, such as nested Views or taxonomy and user Views.
In the meantime you need to use the classic editor for Views.
If you have installed Blocks you may need to go to Toolset > Settings and specify that both the classic and block editing UI should be available.
You can then make a View with the classic editor at Toolset > Views. You can achieve something of a hybrid by using the Loop Wizard to create the scaffolding for the output that uses a content template, and then design that template with Blocks.
Then when it comes to insert the View, you cannot use the View block to insert it.
You need to use a block such as the Classic block, where you will see the old Fields and Views button (behind an icon), which you can use to insert the View and where you will be asked whether you want to display the whole View, just the search, just the results etc.