The below is a summary of all the libraries Nick mentions in his video.

Purpose Open-Source Package Microsoft Alternative
Messaging/Eventing framework MassTransit
Wolverine

(NServiceBus, Rebus too but they are not mentioned in the video)
Upcoming Microsoft Eventing Framework (possibly in .NET 10)
Lightweight Web Framework for building APIs Nancy FX (Archived)
Carter
ASP.NET Core Minimal APIs
OpenAPI Documentation Generation Swashbuckle (Swagger) ASP.NET Core OpenAPI Support
JSON Serialization Newtonsoft.Json System.Text.Json
Dependency Injection Container Autofac
Lamar
Ninject
Unity (DI Framework)
Microsoft.Extensions.DependencyInjection
Hybrid (Local + Distributed) Caching Library FusionCache Microsoft Hybrid Cache (Upcoming in ASP.NET Core)
Actor Model Framework Akka.NET Orleans