The Garrison Hall is the building whose stated job is to increase your units' Tactical Immunity.
One line of building text, and it points at a stat most players never look for.
🏛️ One Stated Job
The Garrison Hall can increase your units' Tactical Immunity. That is the whole line, so I read it as the building's own purpose and not a side effect. Upgrade tasks for it are worded as raising the Garrison Hall to a given level.
🔎 What Is Not Said
The line gives no number, no per level gain, and no unlock requirement. I will not guess at any of them here. If you have upgraded it and watched a screen change, that screen is better evidence than my guess.
🧭 Not A War Room
The Footmen War Room and the Archer War Room have their own separate lines, written for one troop type each. The Garrison Hall is a different building with a different line, so do not read one building's text as another's. 🧱
With one upgrade to spend, do you raise the Garrison Hall for Tactical Immunity, or raise a War Room written for one troop type? 🤔