During the 2022 season, Apple TV+ hosted two “Friday Night Baseball” games each Friday from April 8 to Sept. 23. Those were available in 13 countries, including UK.
The regular baseball season started on April 7, and ended on October 5th.
The post-season games are listed on MLB.com, including which network airs each of the games. You will need separate access to these content providers, or British licensees.
The Sports tab is available in the US and Canada in the TV app on Apple devices. I believe that it would be omitted in most other countries and regions. Although I can’t find an authoritative list.
The Sports tab links to content in external apps (except for FNB) if supported. You would need those separate apps, and any subscriptions to content therein.
In the UK, I think BT Sport carries the MLB games. Unfortunately, BT Sport is not listed as an app that supports being connected to the Apple TV app, meaning you will have to access it from the BT Sport app itself (BT Sport subscription needed).