I've noticed that many archetypes with a level 2 dedication feat simply don't have any level 4 feats. How does this work with the free archetype variant rule? Do you just discard the bonus feat slot at level 4? Also, does playing with this variant rule essentially make it impossible to take a level 4 dedication feat at level 4?
I don't see a specific rule for this, but I would just let them ignore the restriction of picking a certain number of archetype feats before selecting a new archetype. There's nothing preventing you from picking a 2nd level feat at level 4.
You can still take a feat from your regular class at level 4, you don’t need to exclusively pick feats from your archetype once you have its dedication. I was wrong on that, I forgot that you get more free feats as you progress with your free archetype
There’s also nothing stopping you from picking any level 2 feat you’re eligible for at level 4, same goes for dedications. The feat level is really just a minimum level requirement.
You can still take a feat from your regular class at level 4, you don’t need to exclusively pick feats from your archetype once you have its dedication.
No. Feat from free archetype has to be from its dedication and it cannot be skill feat. And unless the GM says otherwise, normally level 4 dedication can't be taken with free archetype at level 2 or 4 (level 6 is possible since in certain dedication you can get 2 feat in level 4).
My question is specifically about playing with the popular "Free Archetype" variant rule. With this variant rule, you gain an extra class feat slot every even level, but the slot can only be used on an archetype feat. That's where my question was coming from.
Playing with free archetype almost inevitably requires making house rules to accommodate it. You level 4 issue can actually start at level 2, as there are sub-classes that can grant a multiclass dedication feat as a class feature, and at least 1 racial feat that can grant a multiclass dedication.