The Search box just searches the whole store, it's doesn't limit it to the part of the store that you are currently viewing. And not all TV programmes are available in from iTunes or in all countries.
You could use this webpage to search for items https://linkmaker.itunes.apple.com
That will give a link to click on which will allow you to view an items's description page on a browser, and which will have a 'view in iTunes' button on the left-hand sde of it to then go to it in the store.
Or there is also a Browse button under Quicklinks on the right-hand side of the store home page :
That will allow you to select TV programmes, the genre, and the programme and series