144h Visa Free

Flights can be ticketed separately and this detail has always been perfectly allowed.

During your first stop in Shanghai, on your flight from Osaka to Australia via Beijing, you will be perfectly covered by 24 hour visa free transit. This is fine.

Anyway, your intention to make a round trip flight from Australia to Chengdu and back is not eligible because there is no third country. The rule is simple and it states that the immediate cities before and after a Chinese destination have to be in different countries. As you can see, your immediate cities are in a single country - Australia.

To be eligible for something like this, you have to introduce a third country or eligible territory, for example Hong Kong. Your eligible itinerary could look like this:

Australia - Chengdu - Hong Kong - Australia

This is one of many examples how an eligible itinerary looks like.