I feel dumb asking this because I feel like I am missing an obvious answer, but in Assembly II (Shards of the Throne expansion) who gets the Speaker token?

The active player (with the Assembly II Strategy card) first decides who will play a Political card from their hand. After that, the active player gives the Speaker token to any player that they want (including themselves). The only limitation is that the person chosen to play a Political card cannot be the same person who is awarded the Speaker token.

Meaning that if you have a political card that you really really want to play, you may not also become speaker.

Also, conversely, if you really really want to become speaker you may not play a political card.

Provided of course that it is you who hold the Assembly II SC....