You can use "custom filters" for this.
To open the interface for creating a new custom filter, you can do the following:
- Navigate to the Home page or Questions page.
- On the right sidebar, below the community bulletin, you will find a panel titled "Custom Filters". There, click on "Create a custom filter".
- Navigate to the Questions page.
- Click on the "Filter" tab, which can be found to the right of the sorting tabs.
Now, you can apply various options to your filter. Don't forget to click on "Save custom filter" once you are satisfied. You can find your saved filters in the "Custom Filters" panel in the right sidebar. If there are new posts matching your filter, then a blue dot appears next to that filter in the "Custom Filters" panel.$\dagger$
For your specific use-case, you might prefer to make the following selections:
- Filter by: "No answers"
- Sorted by: "Newest"
- Tagged with: "My watched tags"
The same process can be used on the Meta site as well.