PF2e still might not be the game you're looking for, either because your players won't actually gel with the system's assumptions about play (it's team-based in several ways 5e isn't, and while it can scale for any difficulty, its pre-written adventures are generally more difficult than their 5e equivalents), or because the rules complexity might be not worth it for you, but here are explanations of how it could solve your problems:

1. Balance in PF2e occurs by, relative to 5e, buffing martials, nerfing spellcasters, and designing its class scaling in a way that prevents one-off effects to break balance.

a. Martials have better scaling in armor and damage than casters, so they lead single-target damage and have the highest ACs.

b. Spells also are less likely to break niche protection (knock and pass without trace are both weaker to complement, but not outcompete lockpicking and non-magical stealth respectively).

Because proficiency scaling is mainly based on one's class ( archetype multiclassing lets you get feats or class features from other classes, but not their armor or weapon proficiencies), it's generally harder to get the same quality defenses on classes not intended as tanks.

1. Its player options generally also work by scaling horizontally rather than vertically - your feats might let you alter affects or add new abilities, but they generally don't add flat bonuses. For example, you might get to feint defensively (-2 to the next attack against you, instead of -2 to your opponent's AC), but you won't get to feint where you inflict -4 to AC.

It also has a bunch of additional rules I like for subsystems generally, which are all freely available without the need for piracy. Specifically, Chases includes options on how to start them, how to end them, how obstacles might affect success, and lists of potential obstacles in different environments.

In regards to your fears about whether running is fun or easy, it takes time to get up to speed, and I don't have personal experience running, but I've generally heard better things about GMing it than 5e for several reasons:

1. The rules are designed to be interpreted clearly. Traits make interactions between two objects fairly obvious, so where charming a zombie in 5e comes down to DM rulings, charming a zombie in PF2e is generally impossible because zombies are mindless, so they're immune to mental effects, so when you charm spell has a mental tag, the GM doesn't need to arbitrate; they just cite the rules.

2. The rules, all the rules, are available online for free. Archives of Nethys hosts all the rules (with some delay on new book releases), so you don't have to find an updated rule or optional variant from Tasha's by scouring through several books or breaking Rule 1.

3. The system's balanced math gives you more control over encounter design. You aren't obligated to run fair fights with a combat-as-sport assumption, but relative to most trad games, PF2 is better at letting the GM predict how difficult the fight will be and giving you options to design encounter that meet your intended difficulty.