BUT, the Availability Tool, Expertflyer and the likes "only" show how many seat the airline is willing to sell on any particular flight. Which in many/most cases are more than the actual number of seats on the flight.
Some tools also show which seats have been prebooked - but many passengers do not prebook their seats and specific seats are thus not assigned to them.
So you can which seats are vacant and how many tickets the airline is willing to sell on any flight at any given time - but not how many seats will be occupied on a given flight.
... just want to know if there is still much space left on board (economy class).
Is this possible? Is there a way to find out? If so, how?....
You need to have access to airlines' internal system to know exactly how many seats are still available. There is no publicly accessible way to know as it is a trade secret. You can try calling SQ directly but they are unlikely to disclose this information.