The Namadgi National Park website of the ACT Environment, Planning and Sustainable Development Directorate, for short ACT Environment, has been updated. They have even provided a rather nice map and updated the walks page, too.
Tharwa is a great idea for a day out and there is a lot to see in a small area. You could consider riding there south through Canberra, or if you are keen then try the loop ride from Stromlo Forest Park south through the suburbs to Tharwa, where you cross the Murrumbidgee River and return to Stromlo Forest Park on the other side of the river via Tidbinbilla Nature Reserve and Cotter.
In 2019 the Environment, Planning and Sustainable Development Directorate (Environment) released the Canberra Nature Park Draft Reserve Management Plan. The Murrumbidgee corridor, the Molonglo River Reserve, the Tidbinbilla Nature Reserve and the Namadgi National Park are not part of Canberra Nature Park. The Canberra Nature Park reserves are ideal for recreational cycling.