Cisco 9300-24UX-E as layer 3 distribution

I have a hospital with a campus style network and a horrible design, they have 3 large buildings all sitting off the back of a stacked 4500-X core and P2P circuits stretching layer 2 to access switches in each of the buildings.

My proposal is to create a resilient OSPF network between the buildings to create a full mesh "triangle" which requires an additional circuit from building 2 to 3. I am planning to use cisco 9300-24UX-E's as the new collapsed cores in each building and run OSPF over it for the resiliency.

Efforts have already been completed to give each building their own VLANs, but they currently all terminate on the core in building 1.

Having never worked with the new Catalyst 9XXX series, I have some questions:

1. Do you agree that this switch I have chosen is suitable? It needs to be mGig copper as they want to save money and also treat it as a server access stack
2. I know these switches stack, but am unsure if I need to buy a stack-kit/stackwise cables (i.e. do they come in the box?? no amount of googling can answer this for me).

The kit needs to be Cisco, as they are a Cisco-only shop and we'd rather keep it that way. But I am open to other suggestions on hardware models, and even constructive feedback on my design. They are very adamant that resilience is key here, hence the full-mesh approach with OSPF to failover the circuits, and the stacked collapsed-core at each building.

The end goal will also to have the most important of the 2 buildings connected via an etherchannelled P2P circuit, but that comes later...