No, your EU, UK, or US mobile plan will not offer free "roam like at home" services when you travel to Kazakhstan.
Traditional international roaming outside of specific regional agreements, such as the EU's "Roam Like At Home" scheme, is typically very expensive. Kazakhstan is not included in these free roaming zones for EU, UK, or US providers, meaning you'll likely face significant pay-as-you-go rates. These can include high charges per megabyte of data used, and for calls made or received, which can quickly lead to an unexpectedly large bill after your trip. Even if your provider offers an international roaming package, these often come with limited data allowances at premium prices.
For reliable and cost-effective internet access during your visit to cities like Almaty or Astana, a local eSIM is a much more economical alternative. It provides immediate data access at local rates, connecting you to the strongest available major network in the country, such as Kcell, Beeline, or Tele2/Altel, depending on your plan and location.