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

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
