Can the superiority die from ‘Superior Technique’ be used for newly learned combat maneuvers?

Question

A fighter receives a superiority die for choosing Superior Technique fighting style, then reaches level 3 and chooses Martial Archetype; Battle Master.

Can the superiority die from Superior Technique be used to perform the maneuvers learned through the Battle Master’s Combat Superiority feature?

The trouble I’m running into is with the wording that the dice are added, yet a player choosing this fighting style at level 1 would not have any superiority dice. Then when you gain combat superiority at level 3 it declares you have 4 dice. This seems to mean the die you would already have from superior technique is overwritten ‘You have four superiority dice’ (and not 5 dice).

Relevant Rules info:

SUPERIOR TECHNIQUE You learn one maneuver of your choice from among those available to the Battle Master archetype… You gain one superiority die, which is a d6 (this die is added to any superiority dice you have from another source). This die is used to fuel your maneu­vers. (Tashas p.41)

And

COMBAT SUPERIORITY When you choose this archetype at 3rd level, you learn maneuvers that are fueled by special dice called superiority dice…

Superiority Dice. You have four superiority dice, which are d8s. A superiority die is expended when you use it. You regain all of your expended superiority dice when you finish a short or long rest. (PHB p.73)

Answer 1

The Superior Technique fighting style is, practically speaking, the Martial Adept feat with one maneuver instead of two. Now, as discussed here the Martial Adept feat has been subject to many confusing errata, but most important is this quote from Jeremy Crawford:

[The improved combat superiority feature] intentionally makes no distinction between a die you get from the class and a die you get from the feat.

In addition, in one of the versions of the errata, the following sentence was added to the feat:

The superiority die is added to any others you have, no matter when you gain them.

Now, this sentence was later rephrased more ambiguously, but it seems that Martial Adept superiority dice are supposed to be identical to the Combat Superiority dice, and used as part of the same pool of dice. This would also imply that Combat Superiority dice can be used for Martial Adept maneuvers. Now, since Superior Technique is basically just a nerfed Martial Adept, down to the words used, I would assume the same conclusion apply to it as well.

TL;DR: You can use your superiority dice however you want, as if you had one more die and one more maneuver in the Combat Superiority feature to begin with.

Answer 2

Yes, and they can use those dice for either the maneuvers from the Battlemaster Subclass or the maneuver granted by the Feat interchangably. This is evident in the text where it says "(this die is added to any superiority dice you have from another source)" - just like the PSI dice from some Tasha's subclass, this is adding a resource that can be spent by any ability that allows you to spend that sort of resource.