I see that you used the Filter for the ins stock status that is possible to add in Toolset Views or archives, which is applying to the Hidden Custom Field which WooCommerce Registers for this:
_stock_status
Then, you insert this as a Radio Field, hence, you will use the GUI "New Filter" to add that.
There, you can choose between existing values, or custom values, for your Radio field in the search.
Change to "Use manually entered values", and then fill as many options you want.
It seems you will need 2:
One for "In Stock" (pass the right Custom Field value for in stock) and another that can be selected for the ones out of stock
This is an either/or decision, but by default on the front end when you load this View or archive the first time it will show that radio as unselected field, hence, show all the products wether in or out of stock
If you want to first load only one kind of products I suggest to enrich the link to the page where this View is (or the archive) (from other places of your site) with the URL parameter required to actually filter the results (the same parameters as the custom search adds after you submit it)
So you could link to the page/archive with an URL like "site.tld/page-or-archive/?url_param_to_listen=value_to_search"
This will automatically show only the products of one kind and you can then still check the other radio so to update those and show the other kind of products.
I'm actually trying a different approach to this now, simply sorting the products by stock status. I want to display all of the in-stock products in a category, followed by the out-of-stock products. I have tried sorting by _stock_status (as a number, string, and native custom field) but cannot get the products to sort. I also tried the field "views_woo_in_stock". That didn't work either. Am I doing something wrong?
I found a code snippet that I can put in my theme's functions.php that does the sorting I want (in-stock products, then out-of-stock products). But I'm still curious about why the sorting doesn't work in my view.
I've enabled the views debug to see whats happening but its not showing any information that would give me an idea as to whats wrong.
Currently creating the backup so i'll report to you once i've got any new information.
In the meantime you can use the code to do the sorting. Also is this the only place your sorting does not work? If you create a simple view and add some form of sorting does it work ?
I discovered a setting under Toolset > Woocommerce Views that I was unaware of, and unchecking the box (see screenshot) seems to have fixed it. I need to make a fresh copy of my staging site as soon as possible. Will that interfere with what you're doing?