You add your wounded value to your dying value when hit
When you initially are reduced to 0 by a attack that deals lethal damage, then you increase your inital dying value by your wounded value if you are already wounded at the time (Core Rulebook, p. 459, Knocked out and Dying):
As a player character, when you are reduced to 0 Hit Points, you’re knocked out with the following effects: (...)
You gain the dying 1 condition. If the effect that knocked you out was a critical success from the attacker or the result of your critical failure, you gain the dying 2 condition instead. If you have the wounded condition, increase your dying value by an amount equal to your wounded value. (...)
If you have both the wounded and the dying conditions and take damage, then you increase the value of your dying condition, and add the value of your wounded condition (Core Rulebook, p. 459):
If you take damage while you already have the dying condition, increase your dying condition value by 1, or by 2 if the damage came from an attacker’s critical hit or your own critical failure. If you have the wounded condition, remember to add the value of your wounded condition to your dying value.1
This is even more clearly spelled out on the DM screen, which explicitly states under Death and Dying for the wounded condition (kudos to @Linus):
Any time you gain the dying condition or increase it for any reason, add your wounded value to the amount you gain or increase your dying value
This is not an artifact of Archives of Nethys, it is on the actual DM screen, and if the Archives of Nethys are keept up to date with the latest versions, not an outdated DM screen:
For example, let's assume you are wounded 1. You get hit by and reduced to 0 by a normal attack, gaining the dying 1 condition, to which you add the wounded 1 value, for a total of dying 2. You now get hit again by another normal attack, increasing your dying value by 1 and again adding your wounded value of 1, bringing you to 4 and killing you.
1I do think the language in the main rules text is somewhat ambiguous, as it tells you to "remember" to add your wounded value to the dying value. This could also be read as as a reminder of the included wounded value, instead of telling you to add the wounded value here again. If you read it like that, the above example would end with dying 3. In a way, you would have a "real" dying value, to which you add your current wounded value at any given time, and if the total is 4 or greater, you die.
A reading that you only add wounded when you initially gain the dying condition in my view is less likely, because when you originally gain the dying condition while wounded, you increase the dying condition value. You don't add the wounded value to your dying condition value. So the sentence telling you to remember adding your wounded value should not refer to that, as you never added your wounding value to begin with. And of course, the DM screen language does away with the ambiguity.
However, this makes combat quite deadly — essentially it means a single hit when wounded and dying will kill you, while if you only apply the wounded value once, when originally gaining the dying condition, you could survive one such hit. If the DM does not like that, they could ignore that rule (or interpret it the other way) and only apply wounded when dying is initially gained.