[Statsig Adpater] migrate from statsig-node-lite to @statsig/serverless-client

[gabrielcolson]

We use the Flag SDK in our NextJS app with the Statsig adapter and the Vercel Edge integration. We tried to setup Statsig session replays but it did not work when bootstraping server side with the instance provided by the adapter because of some missing fields. It appears the package used by the adapter (statsig-node-lite) is no longer maintained and will be deprecated in favor of @statsig/serverless-client (cf screenshot).

We could replace statsig-node-lite and statsig-node-vercel by @statsig/vercel-edge to make sure @flags-sdk/statsig supports the latest Statsig features.