What (if anything) can P2E wildshaped battle form druids do with spells?

Question

I'm playing with a wildshape druid character build, theoretically for the Strength of Thousands campaign. That means the Druid is also getting Wizard as a free archtype, along with a bevy of wizard spells. I'm wondering how to aim this Wizard spellbook.

With D&D 5E I believe it just flat out states you can't cast spells in Wildshape, but P2E doesn't say that. However, it does say this about "battle form"s:

Unless otherwise noted, the battle form prevents you from casting spells, speaking, and using most manipulate actions that require hands. (If there's doubt about whether you can use an action, the GM decides.)

Because of comma placement in this large first sentence (oxford comma, or no?), its unclear to me if this means bf wildshape prohibits all casting, or just casting that requires hands. I'd of course like to assume the latter, but there's probably a ruling on this somewhere that I've been unable to find?

So the question here is what exactly can I do with all my spells while in a wildshaped battle form?

What I'm pretty sure about:

• Carry most buffs that have an effect at the next qualifying event that were cast on me before changing, as long as it doesn't affect my weapons or armor rather than me. eg: Guidance, Barkskin.
• Carry most 24 hour buffs. eg: Mind of Menace
• Sustain pre-cast spells. eg: Pack Attack
• Componentless reactions provided by pre-cast spells (eg: Life Block provided by Protect Companion spell cast just prior to going into wildshape)

What I'm pretty sure I can't do:

• Spells with "material", or "focus" components.
• Spells with the "manipulate" trait.

What I'm unsure about. Includes (but is not limited to):

• Touch spells with only the "somatic" component (based on the fact that these don't require a free hand, just the ability to touch the target).
• Verbal component spells that aren't otherwise prohibited (the polymorphed wolf is using a "Bark of Power", perhaps?)
• Verbal component spells that aren't otherwise prohibited, after taking the Silent Spell action.

Answer 1

Spell Casting Is Prevented

The Polymorph trait states that:

If you take on a battle form with a polymorph spell, the special statistics can be adjusted only by circumstance bonuses, status bonuses, and penalties. Unless otherwise noted, the battle form prevents you from casting spells, speaking, and using most manipulate actions that require hands. (If there's doubt about whether you can use an action, the GM decides.)

There is no ambiguity¹, battle forms prevent you from casting spells of all kinds, including spells that don't require hands.

As you've pointed out, you can benefit from ongoing spells that you cast beforehand, including using actions granted by such spells... as long as said benefit doesn't conflict with the quote above. For example, you can't benefit from Mage Armor's item bonus, and without GM fiat you can't snap your fingers as part of the manipulate action granted by Instant Armor, but problem spells like these are few and far between.

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1. To see why, take a closer look:

the battle form prevents you from casting spells, speaking, and using most manipulate actions that require hands.

In this sentence, 'that require hands' must refer to either the entire list 'casting spells, speaking, and using most manipulate actions' or just 'manipulate actions'.
However, the syntax just doesn't work for the entire list and this becomes especially obvious if we rewrite the sentence in full for each item in the list:

the battle form prevents you from casting spells that require hands, it prevents you from speaking that require hands, and it prevents you from using most manipulate actions that require hands.

Hence, 'that require hands' must refer only to 'manipulate actions'.