dapr-pluggable-component-supabase VS supabase-csharp

I'm not sure that I understand your question. The code I refer to in this blog posts runs locally, but it connects to a Supabase database in the cloud. So no data is stored locally.

This proof of concept implementation of a pluggable component demonstrates how the Dapr pluggable component .NET SDK makes it easier for developers to create their custom components. You can use this solution as a starting point, and expand it with additional state management API features, such as entity tag (ETag), metadata, and options, as described in the specification. A requirement for using this pluggable component in a real project is to deploy it to a (managed) Kubernetes environment or use it in a self-hosted mode.

Supabase is a popular, open-source, Firebase alternative that offers Postgres databases, authentication, Edge functions, real-time messaging and file storage. The Supabase community has released a C#/.NET library that developers can use to integrate their .NET apps with the Supabase platform. For managing Postgres databases, the library uses the postgrest-csharp library that allows developers to use strongly typed models and LINQ queries.

The Supabase C# library also uses Supabase Realtime. So I think you should be able to use it. I haven't tried the realtime part myself yet, only the Postgres part. There are some examples in that repo you could use for inspiration.