I don't use the Solution explorer but I also don't think it has one.
I usually kickstart a fresh application with a SLN and a few projects in the dotnet CLI and VSCodium picks up the launch project automatically when I tell it to create a launch.json. For existing applications, if the .vscode folder already exists it will just pick it up or I can also just ask it to create a launch.json.
That workflow has been ingrained into me since there were no real C# utilities for VS Code when it first launched, so not much changed for me when going to VSCodium.
For the warm and fuzzy feeling I get when I know all my documents, notes, calendars, contacts, passwords, movies/shows/music, videos, pictures and much more are stored safely in my basement and belong to me.
Nobody is training their AI on it, nobody is trying to use them for targetted ads, nobody is selling them. Just for me.