Nope. As a player that has played all versions of D&D since the beginning, PF2 is nothing like 4E. It is far more like 5E. Even that comparison is off. It's more of its own game testing a bunch of new ideas, some of them very interesting, some questionable, and it will take some time to figure out.
Having played all the editions, I have to say PF2E is the closer to 4E than it is to 1E/2E, 3E or 5E. The more PF2E is played, the more it feels like 4E. I haven't gotten to play the final PF2E version yet (there's local resistance in doing so) but it doesn't look much different than the Playtest in terms of how it will feel.
First impressions are telling. 4E if you flip to a class you have all these little boxes and colors around a Power and a litany of keywords... (flipping) like the Warlock's Dreadful Blast, "Arcane, Fear, Implement, Psychic" and this little diamond shape separating that from it's indication it's an "Encounter" power. PF2E is almost identical with how it delineates "powers" and you read through the keyword tagging. 5E, 3E, 2E, 1E read more naturally - it's just a bold ability name and then a non-bold sentence that follows that explains it. PF2E is heavily based on the notion of using the terms "Stride" and "Strike" often at your table, i.e. spending 2 actions (of your 3) but that 2 action cost gives you the ability to make 3 Strides (a horse gallop IIRC). After a few sessions, your brain recalls back when it used to say the word "Shift" aloud more often than would seem reasonable.
The action economy feels roughly 4E-esque. In 4E, I recall folks trying to figure out their "3 action budget" - a standard action and 2 minor actions (or a standard, move and minor, or..). In PF2E, it's kind of similar as players pretty much stand in place and try to figure out the optimal way to spend 3 actions, sometimes with pauses on determining the rough probability of hitting an AC, but now carrying further baggage of probability of a critical hit or critical miss. 1E, 2E and 5E didn't feel like this at all. Folks could move freely without expending a "resource unit" that could be spent in another way.
PF2E is a little worse in a sense because it codifies so many actions, like "Recall Knowledge". You're jumped by skum and their weird crab-monster pet. Do you spend 2 of your 3 actions doing "Recall Knowledge" on those 2 things you're facing? Or do you metagame knowing what to expect because you don't want to spend the precious action that turn and instead get your buffs going? PF2E really gets into combat crunch and if your players are a little OCD and a little math-bent, they'll start to act out-of-character in order to take the more mathematically sound options. 1E, 2E, 5E didn't have this baggage so much as you had all this freedom outside of combat actions to be like your character should be, and then just decide ultimately what you do with that action (which in the 3E era was more powerful if you didn't move and the conversion of a SA to FRA yielded an incremental benefit).
Overall the feel is a bit like it's a Fantasy Boardgame with its own unique ruleset vs a familar D&D coat you've worn before where at a 6-person table there's really only 1 or 2 people who really have mastery over the specialized rules and act as advisors helping the others play through by the rules and try to beat the challenges by helping them play their own characters more optimally. To me, the best D&D editions the casual gamers had more autonomy in their decisions each turn because the variability of in-combat in-turn decisions wasn't so broad. Your friends would encourage, "cast fireball!" at you or "attack it!", which felt more in-character vs explain the precise use of multiple actions, "open with your Swipe, then flourish with your Power Attack!" This is the kind of Pandemic-esque "coaching"play that we had quite a bit of in the 4E era with unwieldy vocabulary terms that led to its shorter table life (there's a technical term for this across all board game genres which escapes me this morning).
EDIT: Quarterbacking. That's the term. PF2E feels like it has more quarterbacking to my groups to put it on par with 4E if not even beyond 4E. (The next edition down in quarterbacking would be 3E, then a big divide before 5E, 2E, 1E).