So currently there's no way to add any Battle Master Maneuvers to your character sheet through the Superior Technique fighting style gained though a fighter's fighting style choice or through the Fighting Initiate feat.

Well there is the Martial Adept feat which does add two maneuvers to your character sheet. It's even integrated with a Fighter's Battle Master maneuver list where if you select one in one method, it's not available in the other method.

But there's an issue with the Martial Adept feat. It doesn't show the limited use tracker for it's 1 superiority die. Below is a screenshot of a Battle Master Fighter 20 showing check boxes for it's 6 superiority dice but no mention of the 1 from Martial Adept.

So we need to fix Martial Adept and create something for Superior Technique.

Both of these methods assuming you have purchased the Player's Handbook or the Martial Adept feat from the dndbeyond store.

Create Martial Adept (fixed):

1. Create a Homebrew feat.
2. Under Use an existing Feat as a template: select Martial Adept.
3. Expand the ACTIONS section.
4. Click on Edit for the Martial Adept action.
5. Change the ACTIVATION TYPE dropdown to Action.
6. Click the blue SAVE button.
7. Change the NAME to Martial Adept (fixed).
8.  Add the following line to the DESCRIPTION: 
   • This feat adds the appropriate action and tracker to your character sheet for the Martial Adept feat.
9. Add the following to the SNIPPET:
   • You learn two maneuvers of your choice from among those available to the Battle Master archetype in the fighter class. If a maneuver you use requires your target to make a saving throw to resist the maneuver's effects, the saving throw DC is {{savedc:str,dex}}. You gain one superiority die per short rest, which is a d6, that is used to fuel your maneuvers.
10. Click the orange SAVE CHANGES button.

Create Fighting Style: Superior Technique:

1. Create a Homebrew feat.
2. Under Use an existing Feat as a template: select Martial Adept.
3. Expand the ACTIONS section.
4. Click on Edit for the Martial Adept action.
5. Change the NAME to Superior Technique.
6. Change the ACTIVATION TYPE dropdown to Action.
7. Change the SNIPPET to:
   • You learn one maneuver of your choice from among those available to the Battle Master archetype in the fighter class. If a maneuver you use requires your target to make a saving throw to resist the maneuver's effects, the saving throw DC is {{savedc:str,dex}}. You gain one superiority die per short rest, which is a d6, that is used to fuel your maneuver.
8. Press the blue SAVE button.
9. (Optional) This will add some prerequisite text but nothing mechanical to enforce.
   1. Press the ADD A PREQUISITE button
   2. Add the following to the DESCRIPTION:
      • Requires the Fighting Style: Superior Technique
   3. Press the blue SAVE button.
   4. Then press CANCEL.
10. Change the NAME to Fighting Style: Superior Technique.
11. Change the DESCRIPTION to:

    • This feat adds the appropriate actions and tracker to your character sheet for the Fighting Style: Superior Technique. 

      ---

      You learn one maneuver of your choice from among those available to the Battle Master archetype. If a maneuver you use requires your target to make a saving throw to resist the maneuver’s effects, the saving throw DC equals 8 + your proficiency bonus + your Strength or Dexterity modifier (your choice).

      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. A superiority die is expended when you use it. You regain your expended superiority dice when you finish a short or long rest.

12. Change the SNIPPET to:
    • You learn one maneuver of your choice from among those available to the Battle Master archetype. If a maneuver you use requires your target to make a saving throw to resist the maneuver’s effects, the saving throw DC is {{savedc:str,dex}}. You gain one superiority die per short rest, which is a d6, this is used to fuel your maneuver.
13. Change TOTAL NUMBER OF FEAT OPTIONS USER CAN SELECT to 1.
14. Press the orange SAVE CHANGES button.

If you do everything correctly, you'll be able to add the feat Martial Adept (fixed) for a variant human, custom lineage, or any ASI improvement and it will show up on your Actions tab correctly. You'll also be able to add Fighting Style: Superior Technique through Manage feats if you take this fighting style as a Fighter or through the Fighting Initiate feat. Your FEATS tab will end up looking like this (if you take both):

And your ACTIONS tab will look like this:

All the maneuvers chosen by either of these will show in their appropriate Actions tab (Actions, Bonus Action, Reactions, No Actions) exactly the same as maneuvers from Battle Master Fighter.

Also building a Variant Human with the Martial Adept feat, Battle Master Fighter with the Superior Technique fighting style for funz. By level:

Level 1

2d6 Superiority dice and 3 total maneuvers.

1. Brace (reaction)
2. Distracting Strike (on a hit)
3. Feinting Attack (bonus action)

Level 3

2d6 and 4d8 Superiority dice and 6 total (3 new) maneuvers.

1. Evasive Footwork (movement)
2. Lunging Attack (part of an action)
3. Ripost (reaction)

Level 7

2d6 and 5d8 Superiority dice and 8 total (2 new) maneuvers.

1. Sweeping Attack (on a hit)
2. Commander's Strike (bonus action)

Level 10

7d10 Superiority dice and 10 total (2 new) maneuvers.

1. Trip Attack (on a hit)
2. Goading Attack (on a hit)

Level 15

8d10 Superiority dice and 12 total (2 new) maneuvers.

1. Precision Attack (part of an action)
2. Rally (bonus action)

Level 18

8d12 Superiority dice and 12 total maneuvers.

This works too well! thanks!

This is something the team of dndbeyond can learn from. Maybe they should add this into their system... Thanks for the fix!