You can stay in the shape of a dragon permanently. The shape. Just because you change into the form of a dragon doesn't mean you are a dragon. You don't live forever or gain the ability to turn into a human; you just get what the spell says you get. You can cast spells, because the spell specifically calls out being able to take manipulate actions. You're using magic to pretend that you're a dragon.
looking at it the only thing dragon form overrides is you have hands and can use them to perform manipulate actions.
otherwise
Polymorph
These effects transform the target into a new form. A target
can’t be under the effect of more than one polymorph effect
at a time. If it comes under the effect of a second polymorph
effect, the second polymorph effect attempts to counteract
the first. If it succeeds, it takes effect, and if it fails, the
spell has no effect on that target. Any Strikes specifically
granted by a polymorph effect are magical. Unless otherwise
stated, polymorph spells don’t allow the target to take on the
appearance of a specific individual creature, but rather just a
generic creature of a general type or ancestry.
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.)
Your gear is absorbed into you; the constant abilities of your
gear still function, but you can’t activate any items.
and dragon is a battle form
Which, since it specifically says it stops casting spells and the dragon form does not say it allows spell casting, you just have the ability to do manipulate actions. Which is pretty sad. But 'balance' I guess.
Sadly, the shapechange spells don't use common sense, they use meta sense. You battle form and unless the spell says otherwise, you get to do nothing but attack with its given attacks.
As Dragons can talk, I don't see why a druid could not cast magic while transformed and to be clear the spell Humanoid form does not say you could talk either.
1. dragons are a battle form, so apperently you don't know how to speak properly with your new mouth *shrug*
2. humanoid form DOES NOT give you a battle form and thus doesn't limit your actions.
As Dragons can talk, I don't see why a druid could not cast magic while transformed and to be clear the spell Humanoid form does not say you could talk either.
Specific rules say, battleforms can not cast spells. I would agree they can talk AND cast spells, but the specific rules say no. Humanoid form is not a battleform so it allows normal actions.
Dragon Form gives you the dragon trait. I don't have the Beastrary infront of me but I think it lists dragons speaking there. thus I would rule being poloymorphed into a dragon would let you speak.