Highlighting Selected Button

Configuration Frontend
4

If the question is for this horiz stack only - then I would suggest to post a code for THIS card only, otherwise it creates a distraction.
And posting a simplified code greatly increases your chances to get a solution fast.
Check this code:

type: horizontal-stack
cards:
  - type: button
    entity: sun.sun
  - type: button
    entity: sun.sun
  - type: button
    entity: sun.sun
  - type: button
    entity: sun.sun

изображение

So, what is the question - you want these buttons to be highlighted on a mouse hover?

type: horizontal-stack
cards:
  - type: button
    entity: sun.sun
    card_mod: &ref_card_mod
      style: |
        ha-card:hover {background: yellow;} 
  - type: button
    entity: sun.sun
    card_mod: *ref_card_mod
  - type: button
    entity: sun.sun
    card_mod: *ref_card_mod
  - type: button
    entity: sun.sun
    card_mod: *ref_card_mod

изображение