dlld's page

"If you’re Avoiding Notice at the start of
an encounter, you usually roll a Stealth check instead of a
Perception check both to determine your initiative and to see
if the enemies notice you (based on their Perception DCs, as
normal for Sneak, regardless of their initiative check results)."

Important part is that its success is based vs perception DC not a roll.

DC = perception + 10

Party all uses Avoid notice, they all for simplicity sake roll a 16 stealth and initiative combined per avoiding notice.

The enemies perception DC is 15. The enemy does not notice the party.

The enemies then roll perception as their initiative, they all roll 17s, they have higher initiative but they fail to spot the party as nowhere does it say that perception initiative also acts as a detection roll for stealth that i can find, stealth is always 'contested' with the DC as far as i can tell.

Same goes for seek being contested with a stealth DC rather then contesting the actual stealth roll.

"The GM attempts a single secret Perception check for you
and compares the result to the Stealth DCs of any undetected
or hidden creatures in the area"

So if I'm reading the rules correctly, it's entirely possible for either a PC or a monster to fail to notice the other side but still be first in initiative. For simplicity sake lets just take this into a context of 1 vs 1.

If so, what happens then? I can't find anything substantial about being 'surprised' do i just assume at the start of an encounter the stealthing side becomes 'undetected' rather then 'unnoticed' by the entity who rolled a higher initiative so he can reasonably start using his actions to seek? Given there is no exploration version of seeking as far as i can tell, it's purely a encounter thing and not something a guard would 'spam' his entire watch every 6 seconds so it'd make no sense for him to suddenly randomly begin to seek if absolutely nothing tipped him off.

Or does the one who rolled highest initiative just stand there twiddling his thumbs completely unaware of the impending threat and ignore his turn?