Add support for `willDeleteFiles`/`didDeleteFiles` to tsserver

Suggestion

🔍 Search Terms

willDeleteFiles/didDeleteFiles
update errors after deleting file
deleting file
removing file
renaming file

✅ Viability Checklist

My suggestion meets these guidelines:

• This wouldn't be a breaking change in existing TypeScript/JavaScript code
• This wouldn't change the runtime behavior of existing JavaScript code
• This could be implemented without emitting different JS based on the types of the expressions
• This isn't a runtime feature (e.g. library functionality, non-ECMAScript syntax with JavaScript output, new syntax sugar for JS, etc.)
• This feature would agree with the rest of TypeScript's Design Goals.

⭐ Suggestion

Add support for willDeleteFiles/didDeleteFiles (https://microsoft.github.io/language-server-protocol/specifications/lsp/3.17/specification/#workspace_willDeleteFiles)
As for my current knowledge, tsserver right now watches filesystem on its own, as mentioned in this article. Unfortunately this method is not always correct and sometimes (specifically in larger repositories) after renaming files, or deleting them - tsserver does not know that the filesystem was changed resulting in out-of-sync error messages.
Adding support for such methods would allow editors to notify tsserver that something has changed and then tsserver could internally update it's state about the files.

📃 Motivating Example

https://github.com/microsoft/TypeScript/assets/35625949/1eec8678-8af6-43d0-bf2f-25eecbac0b96

In this example, when file is deleted by the user, the diagnostic about file not existing is not shown. It might be shown after some time in the future, but an editor can send this notification to the server immediately after user performs an action

💻 Use Cases

For now the only way to deal with this is to restart tsserver. While this solution works it would be nicer user experience for this to happen automatically.

Start by reviewing tsserver's filesystem-watching behavior and the linked Language Server Protocol specification for workspace file deletion notifications. Trace how file deletion and renaming currently reach tsserver, then determine the notification handling needed. Done means editors can notify tsserver through willDeleteFiles/didDeleteFiles and its diagnostics stay synchronized without requiring a restart.