python: Replace pyright with basedpyright (#35362)

Follow-up to #35250. Let's experiment with having this by default on
nightly.

Release Notes:

- Added built-in support for the basedpyright language server for Python
code. basedpyright is now enabled by default, and pyright (previously
the primary Python language server) remains available but is disabled by
default. This supersedes the basedpyright extension, which can be
uninstalled. Advantages of basedpyright over pyright include support for
inlay hints, semantic highlighting, auto-import code actions, and
stricter type checking. To switch back to pyright, add the following
configuration to settings.json:

```json
{
  "languages": {
    "Python": {
      "language_servers": ["pyright", "pylsp", "!basedpyright"]
    }
  }
}
```

---------

Co-authored-by: Piotr Osiewicz <24362066+osiewicz@users.noreply.github.com>
Co-authored-by: Lukas Wirth <lukas@zed.dev>

crates/languages/src/python.rs

@@ -35,7 +35,7 @@ use std::{
     sync::Arc,
 };
 use task::{ShellKind, TaskTemplate, TaskTemplates, VariableName};
-use util::ResultExt;
+use util::{ResultExt, maybe};
 
 pub(crate) struct PyprojectTomlManifestProvider;
 
@@ -1619,23 +1619,37 @@ impl LspAdapter for BasedPyrightLspAdapter {
                     }
                 }
 
-                // Always set the python interpreter path
-                // Get or create the python section
-                let python = object
+                // Set both pythonPath and defaultInterpreterPath for compatibility
+                if let Some(python) = object
                     .entry("python")
                     .or_insert(Value::Object(serde_json::Map::default()))
                     .as_object_mut()
-                    .unwrap();
-
-                // Set both pythonPath and defaultInterpreterPath for compatibility
-                python.insert(
-                    "pythonPath".to_owned(),
-                    Value::String(interpreter_path.clone()),
-                );
-                python.insert(
-                    "defaultInterpreterPath".to_owned(),
-                    Value::String(interpreter_path),
-                );
+                {
+                    python.insert(
+                        "pythonPath".to_owned(),
+                        Value::String(interpreter_path.clone()),
+                    );
+                    python.insert(
+                        "defaultInterpreterPath".to_owned(),
+                        Value::String(interpreter_path),
+                    );
+                }
+                // Basedpyright by default uses `strict` type checking, we tone it down as to not surpris users
+                maybe!({
+                    let basedpyright = object
+                        .entry("basedpyright")
+                        .or_insert(Value::Object(serde_json::Map::default()));
+                    let analysis = basedpyright
+                        .as_object_mut()?
+                        .entry("analysis")
+                        .or_insert(Value::Object(serde_json::Map::default()));
+                    if let serde_json::map::Entry::Vacant(v) =
+                        analysis.as_object_mut()?.entry("typeCheckingMode")
+                    {
+                        v.insert(Value::String("standard".to_owned()));
+                    }
+                    Some(())
+                });
             }
 
             user_settings