Sarva-Siddhānta-Saṅgrahaḥ (also known as Sarva-darsana-siddhanta Sangrah) is definitely a work of Adi Shankara. In fact, Adi Shankara followed up this work with the Sarva Vedānta Siddhānta Sāra Saṅgraha, which is the collection of all vedanta works. Further, this was the inspiration of Swami Madhavacharya Vidyaranya of the Sringeri pontiff in 1331 AD to compile all siddhantas together in his work, Sarva-darsana Sangraha. In fact, he quotes from this book indirectly using the same sutras for certain philosophies. The book is also quoted by Madhusudana Saraswati. Therefore, one can conclude this is a work of Adi Shankaracharya.
Now, coming to your next question, Veda Vyasa Siddhanta is different from Vedanta Siddhanta. The veda vyasa siddhanta discussed in this work is actually similar to the Samkhya philosophy. This philosophy is given by Vyasa in the Mahabharata and has nothing to do the philosophy of the vedanta sutras by badarayana.
THE SYSTEM OF VEDAVYASA.
Now, the essence of the Vedas, which has been given out by Vyasa in the Mahabharata so as to be in agreement with all the Sastras, is in
fact derived from the system of the Sahkhyas by the believers in the
This world is made up of two things, namely, the Purusa and the prakrti, The higher (of these two), abiding in the 'city' made up of
the rudimentary elemental principles, is held to be the purusa.
One has to note that Shankara differentiates between the works of Vyasa in Mahabharata from the work in vedanta sutras. Bādarāyana was the Guru (teacher) of Jaimini and is the composer of the vedanta sutras. Some say he is different from Vyasa of Mahabharata. But tradition holds they are the same. Leaving that aside, Shankara differentiates between the vyasa kara mata and bhasya kara mata. Therefore, an explanation is required as why Shankara differentiates between the two philosophies. Madhusudana saraswati explains why in great detail but suffice it to say this is given in some detail in pages xv-xviii of the book you reference.