Design Studio docs search should default to Design Studio docs

When using the search function in QDS documentation, the search result should by default show only results from QDS docs, with option to search other domains as it is currently (i.e. All documentation, Qt5, Qt6, Qt for Python, Qt for MCU).

Steps to repro:

1. go online to Qt DS docs
2. type in 'States' to search box

Expected result:

• Search results are filtered by DS first

Actual outcome:

• You get results from everything else

Reference: do similar search in qt.io/blog