With Sonos you won’t have any lag.

What I would be concerned about is having a decent WiFi signal in each space. Without that you might see music dropouts.

Personally I use multiple Access Points wired back to my main (Not WiFi) router to get the signal where it is needed.

I would think most high quality mesh systems that support a wired connection to the remote units could serve your needs. Probably best addressed in a WiFi specific forum as they would have folks more experienced in difficult setups.

For the long term you should consider running network cable and fiber optics between buildings. You’ll probably want to run multiple access points in each building since all the walls are concrete. Each of these should be wired.

I use wired (Ethernet) connection of the satellites back to my main router. The connection is called a “wired backhaul” as opposed to a “wireless backhaul” that typically uses the 5Ghz or 6Ghz band to establish the mesh. 

The brand of router I use is ASUS.  ASUS has what they call an AiMesh Configurator that sets the proper parameters to establish the mesh. I use three (3) ASUS ZenWiFi Pro ET12 routers with one acting as the main. 

Copied from the ASUS website:

• AiMesh connects multiple compatible ASUS routers to create a whole-home mesh WiFi network. The flexible and scalable technology lets you mix different AiMesh-compatible routers, and add new ones at any time to improve coverage.* All devices in an AiMesh network enjoy access to all the features of the main router, including gaming features, AiProtection commercial-grade security and more. Most ASUS routers already support AiMesh.

Learn more about ASUS AiMesh here.