Do you need an empty hand to cast spells?

Question

The Weapon Storm spell has a somatic component¹ (CRB p384):

[...] This damage has the same type as the weapon and uses the same die size. Determine the die size as if you were attacking with the weapon; for instance, if you were wielding a two-hand weapon in both hands, you’d use its two-hand damage die.

A weapon with the two-hand property can be used with 2 hands, but it is not required.
How can I use a somatic component while holding a weapon in 2 hands?

Is it possible with any spell?

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1) And verbal, but that doesn't matter now.

Answer 1

You can cast any spell while holding anything

Somatic components (CRB, p303):

You can use this component while holding something in your hand, but not if you are restrained or otherwise unable to gesture freely.

Answer 2

While gesturing with fingers while holding a sword is definitely possible, doing it with an item heavy enough to require two hands seems unwieldy at best.

Honestly, the first thing that came to my mind was Bewitched. Yes, the campy show from the 60's. A nose wrinkle was the rather gimmicky somatic element used by protagonist Samantha.

From the same era, Jeannie of I dream of Jeannie had a head nod in addition to folding her arms. Sans folded arms, both above are gestures easily performed with occupied hands.

We generally think of tracing runes in the air with hands or fingers for the required gestures, but GM's discretion is rule #1, and your magic doesn't need to look like everybody else's magic. Even different casters in the same environment can channel the same energies in very different ways.