First, I wasn't directly addressing which was easier, just whether the extra muscles you use while standing allow you to push more weight...you use the exact same muscles to push while sitting or standing.
Second, it is true, but you got it backwards...I'd argue the standing is harder, since you're haing to also focus on stabilizing. We agree, unless I'm interpreting you wrong too.
Yes, we agree. For some reason, I got your username mixed up with terry.dang.rn who was saying standing press is easier than sitting press.
Just for the record, the reason why standing press is harder than sitting presses and the back squat is harder than a leg press machine is because the total weight you can move will be limited to your weakest muscle in use.
In my example, my quads, glutes and hams are much stronger than my core and back so isolating my strong muscles allows me to move more weight. (and standing partially includes my own body weight)
The same principle applies to standing press vs sitting press.
Of course this is generalization and doesn't apply to every weight movement or scale of weight.