Is it really this complicated? True Strike requires a weapon with a cash value of 1cp or more.
Unarmed Strikes (and natural weapons)
These are excluded. There's no good reason, and yes it shuts down some builds. This is a case the spell author will have considered. They want a weapon, and it's clear what's intended. Maybe there is some monk shenanigans that they wanted to avoid. It isn't a surprising decision, though. There are all sorts of unspoken restraints on weapons in the PHB (why can't finesse weapons do bludgeoning damage, for instance? why can't rouges get sneak attack with their fists?). This is far from the biggest constraint on the weapons table.
Shadow Blade.
Also excluded. It's a 2014 spell that hasn't been ported to 2024 yet. I totally understand, though, why it would be excluded, since it does so much more damage than any other finesse, light, or thrown weapon (to say nothing of the advantage).
Flame Blade.
Also excluded. This spell has been updated, and the blade requires a Magic action to use. That makes it incompatible with Casting True Strike. If they re-write the Shadow Blade for 2024, I suspect they would use this kind of wording.
Pact Blade.
This is the only potential ambiguous case. You "conjure...a Simple or Melee weapon." I would say that the weapon you conjure has the value of the same weapon listed in the PHB. Is there any reason to think it doesn't? The fact that you have not paid for the weapon doesn't matter (if you steal a sword, it still has a cash value). You can also (without any ambiguity) bond with a magic weapon, which gives additional damage.
This means that it is possible to use True Strike with at least some pact weapons, and I would say with all. That would allow you to use Charisma to attack (already true of the pact weapon), you can do radiant damage (already true of a pact weapon), and do extra damage at levels 5, 11, and 17. If you do that extra damage, however, it is only a single attack, and could not benefit from Thirsting Blade and Devouring Blade (though you can from Eldritch Smite and Life Drinker).
Now that warlocks can take multiple pacts, the True-Strike option is a reasonable choice for those for whom the Pact Blade is not primary. It is less feat intensive than taking Thirsting/Devouring, but allows a reasonable amount of damage. The benefits of True Strike with a pact blade are (a) increased choice of damage type [fun], (b) proficiency with an otherwise inaccessible Martial weapon [perhaps +1 or +2 damage], (c) he ability to make it appear and disappear [cosmetic], and (d) if True Strike is learned with certain background feats to use Intelligence or Wisdom as an attack stat [this will be very rare]. That's certainly worth an invocation, but it's not a must-have.
Whatever the DM decides on this, at least some pact weapons do count, and there seems to be no obstacle to all pact weapons, even with a strict reading of the 2024 rules. Arguably, this makes a one-level dip into Warlock desirable for some builds.
Artefacts.
This one I do not understand. Why would "without a listed price" correspond to "worth less than one copper piece"? English distinguishes "priceless" from "valueless" easily, and it appears wilful to think that an artifact would not qualify as a weapon worth more than 1 cp.
Wraps of Unarmed Prowess.
Here's one that hasn't been discussed yet. This was a magic item in the Book of Many Things, which came out just before the 2024 rules. In it, Monks can get +1 to +3 to their unarmed attacks, but it's not a weapon (it's a Wondrous Item) and so it does nto change the exclusion of unarmed strikes.
