Deduction says that True Resurrection wouldn't work here.
The concept of souls is referenced in multiple spells, creatures and creature attacks. However Soul itself is not mechanically defined.
True Polymorph makes no mention of souls in the creature being created. True Resurrection requires:
If the creature's soul is free and willing, the creature is restored to life with all its hit points.
A creature having a soul is implied if a requirement is that it's soul is free and willing. From a logical standpoint then no soul = no resurrection.
Souls are not a defined mechanic, but get referenced in spells and creature attacks.
I would generally equate soul having with living creature/humanoid (Including living constructs like warforged).
Other similar spells specify soul related mechanics, for example Clone:
This spell grows an inert duplicate of a living, Medium creature as a safeguard against death...
...At any time after the clone matures, if the original creature dies, its soul transfers to the clone, provided that the soul is free and willing to return. The clone is physically identical to the original and has the same personality, memories, and abilities, but none of the original's equipment. The original creature's physical remains, if they still exist, become inert and can't thereafter be restored to life, since the creature's soul is elsewhere.
In this case the soul is specifically needed to be transferable to the new body which when created is souless and if the soul inhabits the new body you can't resurrect the original.
Magic jar is murky because it is allowed to target "any humanoid" but also specifies a soul swap so I would infer that while it doesn't specify living.
You can attempt to possess any humanoid within 100 feet of you that you can see (creatures warded by a protection from evil and good or magic circle spell can't be possessed). The target must make a Charisma saving throw. On a failure, your soul moves into the target's body, and the target's soul becomes trapped in the container. On a success, the target resists your efforts to possess it, and you can't attempt to possess it again for 24 hours.
Monsters such as the Devourer are an example of creatures targeting soul