How do minions interact with Stunned and Slowed?

[Captain Morgan]

And what about animal companions that get one action when they aren't commanded?

[thenobledrake]

If the character with the companion is stunned or slowed, they just have less actions with which to choose to command their companion.

If the companion is stunned or slowed, it has less actions as declared by the condition, whether or not its commanded.

Why would that work any other way?

[Mellack]

That is probably the way it is meant to work, but a strict RAW reading of slowed will not do anything to a companion. "When you regain your actions at the start of your turn, reduce the number of actions you regain by your slowed value. Because slowed has its effect at the start of your turn, you don’t immediately lose actions if you become slowed during your turn." Note it specifically points out this happens at the start of the turn. "Your animal companion has the minion trait, and it gains 2 actions during your turn if you use the Command an Animal action to command it." The companion doesn't get actions until during the turn. While I would run it as slow affecting those gained actions, there can be a fair argument for saying slow doesn't.
Stunned simply says "Each time you regain actions", so that would definitely effect any actions granted to a companion.