As a user
I want to be able to search elements as I type on the Database activity
so I don't need to wait for the page to reload

Improve Database activity simple search feature, so the entries listed are filtered to show only entries that fit the searching.

Basic 'search as you type' is implemented already in many Moodle pages such as Content Bank, Activity chooser, etc. But apart from hiding/showing entries based on what the user types on simple search input we also need to change and adjust pagination to the results.