I don't think Yandex DCs are used directly for military purposes much. It's more about harming Russian economy in general, including its highly prided digital infrastructure
Also Russia has been targeting Ukrainian digital infrastructure so they make these things fair game IMO.
I don't have specific information about Yandex but don't forget how heavily involved Amazon were with things like: https://www.nytimes.com/2022/12/19/world/europe/ukraine-cybe... it wouldn't be a huge stretch to suggest that a lot of cloud hosting providers are neck deep in national security.
Military personnel use the same Yandex services as regular people: delivery, maps, taxi, etc.
Also Yandex is a large cloud provider, they host a lot of government-connected companies.