Sources Say Yes… unless you think that’s too strong.
Broadly speaking, it seems pretty clear that the idea of Stun is that Stun X is going to cost the character X actions. Having a Stun 1 on their turn cost the character as many as 3 actions is a significant increase to the power of the effect… and that actually has some meaning here, beyond vague handwaving claims someone might make about RAI
Core Rulebook, Page 444 says
Sometimes a rule could be interpreted multiple ways. If one version is
too good to be true, it probably is. If a rule seems to have wording
with problematic repercussions or doesn’t work as intended, work with
your group to find a good solution, rather than just playing with the
rule as printed.
At the same time, we know what the actual intended rules are, as they’re laid out pretty clearly in the sidebar on Gaining and Losing Actions, also in the core rulebook (page 622, I think)
Quickened, slowed, and stunned are the primary ways you can gain or
lose actions on a turn. The rules for how this works appear on page
462. In brief, these conditions alter how many actions you regain at the start of your turn; thus, gaining the condition in the middle of
your turn doesn’t adjust your number of actions on that turn. If you
have conflicting conditions that affect your number of actions, you
choose which actions you lose. For instance, the action gained from
haste lets you only Stride or Strike, so if you need to lose one
action because you’re also slowed, you might decide to lose the action
from haste, letting you keep your other actions that can be used more
Some conditions prevent you from taking a certain subset of actions,
typically reactions. Other conditions simply say you can’t act. When
you can’t act, you’re unable to take any actions at all. Unlike slowed
or stunned, these don’t change the number of actions you regain; they
just prevent you from using them. That means if you are somehow cured
of paralysis on your turn, you can act immediately.
The rules also indicate that you lose any leftover actions/reactions at the beginning of your next turn.
So the rules as written indicate that if you start your turn, take a swing with one action and get hit by a Stun 1, then your two remaining actions sit there useless (unless you can somehow cure that stun on your turn), and if you still have a reaction it is likewise useless. At the beginning of your next turn, you lose the leftover actions/reaction as normal, and regain a fresh set, with one less action because of the stun. The stun, at that point, goes away.
If you feel that that’s not working as intended, however, or that it has problematic repercussions, you are expected to “work with your group to find a good solution”. Alternately, as the GM, you could tweak the rule for yourself, either for this creature, or as a general houserule on the effects of Stun during someone’s turn.