Click the Search bar, click Advanced Search (may take a moment to load). Along the right side is a number of criteria you can filter by, Demos is under Show Selected Type section

Or click here to open the Advanced Search
https://psteamproxy.yuanyoumao.com/search/?term=

Unfortunately there is no way to filter/exclude things from the search bar itself.

You can remove free to play games. Did you see if it removes demos too?