cicd: fix aws eks login for stg/prod deploys

[bogdan-1337]

Description

• Fix aws ecr login for staging/prod, enable docker build github cache and fix naming for some steps.

New stuff ✨

• New stuff goes here

Changes 🏗

• Changes go here

Deletions ⚰️

• Deletions go here

TODO

• [ ] Add TODOs

(Resolves | Contributes to) #31415