Search results – 404 error after hitting enter

It appears your search is going to https://youthtalkedinburgh.co.uk/?post_type[]=&s=sport instead of the (more proper) https://youthtalkedinburgh.co.uk/?s=sport, which works. Looking at the source, it appears your search form looks like this (simplified):

<form  ... >
<input type="hidden" name="post_type[]" value="">
<input name="s"... >
...
</form>

That <input type="hidden" name="post_type[]" value=""> input field doesn’t seem to belong. I suspect either your theme or a plugin is inserting it, but I couldn’t begin to guess which one.

You may still have to take this up with the theme’s support team (or a plugin’s support team), but at least you’ve got a place to start looking.