pathfinder 2e – Hiding without using Hide action

As a small matter, your Rogue isn’t actually hidden, but undetected, since the wall prevents the enemy from seeing the Rogue at all and the enemy has no idea what square the Rogue would be in behind the wall. Undetected starts with:

When you are undetected by a creature, that creature cannot see you at all, has no idea what space you occupy, and can’t target you,

Having a wall between the Rogue and an enemy usually makes it so that the enemy cannot see the Rogue (obviously some special senses can get around this). If you’re Rogue were to have some way to see through the wall and shoot the enemy (some Ethereal Sight and Ethereal Arrow combo, perhaps, that I’m not aware of), the enemy would be flat-footed. From Undetected:

When you’re undetected by a creature, that creature is flat-footed to you.

This means that your Rogue can indeed Sneak somewhere while still (pending a Stealth roll) being Undetected. Note, they have to end their movement with some form of cover, concealment, or invisibility; see this line from Sneak:

You don’t get to roll against a creature if, at the end of your movement, you neither are concealed from it nor have cover or greater cover against it. You automatically become observed by such a creature.

So simply running behind a wall is rarely going to actually give the Rogue a chance to make a Sneak Attack, assuming they have nothing else to hide behind. But it does grant them the ability to Sneak, since they’d be Undetected at the start of their movement. From Sneak:

At the end of your movement, the GM rolls your Stealth check in secret and compares the result to the Perception DC of each creature you were hidden from or undetected by at the start of your movement.

Yes, pending the normal Sneak caveats. Although your Rogue is actually Undetected at the start of their turn, not simply Hidden.