Do I need a transit visa from Shanghai to Serbia via Bangkok and Dubai?

No need.

No need for a transit visa. You don’t even need to check in at the waiting room when connecting flights, so you don’t need a transit visa at all.

If you are transiting in the United Arab Emirates, first of all, they are visa-free for China, so you don’t need to worry about visas. Secondly, they don’t know about the mutual exemption between China and Serbia, so you should prepare the round-trip air tickets and the official notice of Serbia’s visa-free for China!