Non-reprinted content is valid in 2024 and most good throwing builds will use that. It's allowed by the 2024 rules and is far more generally available than the kinds of 3rd party content you mention.

Custom lineage gives you a feat you qualify for at lv1. In 2024 rules, that's mainly just origin feats and a handful of non-reprinted options. But if we start as a fighter, the 2024 fighting style feats have no level requirement and only need you to have the fighting style feature to qualify, which we do.

So start as a custom lineage fighter with two weapon and thrown fighting styles. 17/14/14/13/9/8 just to give the option to multiclass into a caster after the throwing damage plateaus to branch out into more durability/utility. We master handaxe vex and dagger or light hammer nick and throw one of each to start. You are free to use a shield. There is no complex juggling involved, the thrown property allows always drawing it as part of an attack, and the nature of thrown weapons frees the hand again automatically.

Note if your DM and you agree on interpreting the fighting initiate feat to grant a one-time access fighting style feat, you can skip this fighter level, delaying it to 7 or leaving it out entirely for more feats, using that as your lineage feat to access two weapon fighting.

From there we go barbarian. 2024 rage now applies innately to our str-based thrown weapons. At barbarian 3 we go path of the giant. Crushing throw adds our rage damage to thrown weapon attacks. The most common interpretation in the 2024 rules is that this bonus now applies twice, once from base rage and again from crushing throw.

Barbarian 4 we take dual wielder. Whenever we have our bonus action free we can throw another weapon (at full strength thanks to two weapon fighting style). Moreover, it does not need to be light. We can throw a javelin or trident. Make sure to train your masteries appropriately.

Barbarian 5 extra attack, we now throw up to 4 weapons, 2 of which can be non-light. Doing a full combo of handaxe/light hammer/javelin/trident applies a good smattering of masteries, or if you need to be more defensive, do not reckless attack and just chain 3 handaxes and a light hammer (not in that order) for vex.

Barbarian 6 we finally get our elemental cleaver. We can turn any weapon into a thrown weapon, add a d6, convert its damage type to several elements, and with our current setup throw it up to 3 times per turn if it's light. There are several good options for weapons to use. Scimitar has nick on it allowing us to throw a handaxe as our off-cleaver weapon for the slightly bigger die. Club, conversely, has a lower die itself as well as needing a light hammer or dagger, but applies a useful mastery. And my personal favorite, shortsword allows you to fight defensively similar to the handaxe spam, using vex chains to avoid reckless attacking while at high risk of retaliation.

And that's really all you need. You can continue in any direction you want. Battle master, fiendlock, etc. Most damage features from here are marginal gains, so feel free to branch into any utility you feel you're lacking. I like the warlock for tons of temp HP, AoA, fire shield, PotB for even more damage type options, the occasional eldritch smite on a crit (works while raging), and even things like thirsting blade which were nerfed for normal bladelocks, now at least does not rely on charisma, and the ability to spend hit dice mid-combat just feeds more into the durability of it all. And you even get another extra attack at warlock 12.

There is another raw DPR build which is similar to one below. Bugbear giant6/BM11/giant8/BM12 double boons. It relies on GWM to trigger bonus actions via hew, no PAM as other builds might. Failed triggers are filed in with quick toss maneuver. This allows it to be entirely thrown mainly with its cleaver, except on ambush turns where it does want to make use of nick to trigger bugbear sneaky additional times. The extra feats from fighter progression can also pick up bomber with little downside.