When searching with Google for "Climb Sydney Harbour Bridge", pretty much every result say it costs $185.
Only Wikivoyage talks about a free climb (although they also talk about the one above):
You can walk over the bridge. The views are great and admission is free. On the southern side the entrance is hard to find. The entrance on the western side is on Fort St near Observatory Hill. On the eastern side the entrance is on Cumberland St, but if coming from the city Cumberland St is closed at the Wynyard side. Walk along Harrington St and follow the small, hardly noticeable signs past Susannah Place. You can also get the lift up to the Cahill Expressway from Circular Quay, and walk around in about 10 minutes. Don't follow the road signs or any roadway on to the Bridge. You may be intercepted by police before you meet a worse fate with the traffic. The entrance at the northern side is easy to find, about 30 m south of the Milsons Point Station. There is no way to access the bridge by foot without using stairs. There are many flights at Milsons Point and Cumberland St, and two flights from the Cahill down to the bridge platform. If you aren't good with stairs, take the walk next to the harbour. If you want to drive to the walk, there is extremely limited parking in Cumberland St and around the Rocks. Limited 2 hr meter parking is also available near the northern entrance at Milsons Point. The walk is often busy, but there are no queues or crowds. You can walk one way, and take the train the other way if you wish.
Is it the same thing, just without the group/coaching?
Or is it a "light" version, that is - not going to the top?