Full text ticket search

The Freshdesk agent site allows searching for tickets given some text contained within the ticket fields.

Apparently the site loads this data from https://novasys.freshdesk.com/api/_/search/tickets - with other words, not a URL of the v2 API.

I could not find a V2 API method that would allow some kind of full text search. Filter Tickets does not seem appropriate (at least I don’t understand how to use it for such searches).

How can I do full text searches (subject, body, …) using the API?

I would be helpful if I could at least search by part of the subject - is that possible?