What strategy do you use to deploy serverless (lambda, step functions, etc) code?

All of the above - canary, blue-green, and rolling are not mutually exclusive things. They are different techniques to address different aspects.

Start with tiny load on canary to detect early issues, then go to blue-green to start seeing the effect of realistic load on new system, before cutting over full load to the new system.

And the canary and blue green deployments can both use rolling deployments to avoid downtime.

Zappa