Respect --project in uv format (#15438)

Closes https://github.com/astral-sh/uv/issues/15431

This is my first contribution, so I'm sorry if I miss something! Didn't
update any documentation nor added tests. Tell me if this is needed for
this feature 😄

I will try to address https://github.com/astral-sh/uv/issues/15430 in
another PR

crates/uv/src/commands/project/format.rs

@@ -1,3 +1,4 @@
+use std::path::Path;
 use std::str::FromStr;
 
 use anyhow::{Context, Result};
@@ -18,6 +19,7 @@ use crate::settings::NetworkSettings;
 
 /// Run the formatter.
 pub(crate) async fn format(
+    project_dir: &Path,
     check: bool,
     diff: bool,
     extra_args: Vec<String>,
@@ -53,6 +55,7 @@ pub(crate) async fn format(
         .context("Failed to install ruff {version}")?;
 
     let mut command = Command::new(&ruff_path);
+    command.current_dir(project_dir);
     command.arg("format");
 
     if check {

crates/uv/src/lib.rs

@@ -2193,6 +2193,7 @@ async fn run_project(
             let cache = cache.init()?;
 
             Box::pin(commands::format(
+                project_dir,
                 args.check,
                 args.diff,
                 args.extra_args,

crates/uv/tests/it/format.rs

@@ -55,6 +55,75 @@ fn format_project() -> Result<()> {
     Ok(())
 }
 
+#[test]
+fn format_relative_project() -> Result<()> {
+    let context = TestContext::new_with_versions(&[]);
+
+    let pyproject_toml = context.temp_dir.child("project").child("pyproject.toml");
+    pyproject_toml.write_str(indoc! {r#"
+        [project]
+        name = "project"
+        version = "0.1.0"
+        requires-python = ">=3.12"
+        dependencies = []
+    "#})?;
+
+    // Create an unformatted Python file in the relative project
+    let relative_project_main_py = context.temp_dir.child("project").child("main.py");
+    relative_project_main_py.write_str(indoc! {r#"
+        import sys
+        def   hello():
+            print(  "Hello, World!"  )
+        if __name__=="__main__":
+            hello(   )
+    "#})?;
+
+    // Create another unformatted Python file in the root directory
+    let root_main_py = context.temp_dir.child("main.py");
+    root_main_py.write_str(indoc! {r#"
+        import sys
+        def   hello():
+            print(  "Hello, World!"  )
+        if __name__=="__main__":
+            hello(   )
+    "#})?;
+
+    uv_snapshot!(context.filters(), context.format().arg("--project").arg("project"), @r"
+    success: true
+    exit_code: 0
+    ----- stdout -----
+    1 file reformatted
+
+    ----- stderr -----
+    warning: `uv format` is experimental and may change without warning. Pass `--preview-features format` to disable this warning.
+    ");
+
+    // Check that the relative project file was formatted
+    let relative_project_content = fs_err::read_to_string(&relative_project_main_py)?;
+    assert_snapshot!(relative_project_content, @r#"
+    import sys
+
+
+    def hello():
+        print("Hello, World!")
+
+
+    if __name__ == "__main__":
+        hello()
+    "#);
+
+    // Check that the root file was not formatted
+    let root_content = fs_err::read_to_string(&root_main_py)?;
+    assert_snapshot!(root_content, @r#"
+    import sys
+    def   hello():
+        print(  "Hello, World!"  )
+    if __name__=="__main__":
+        hello(   )
+    "#);
+    Ok(())
+}
+
 #[test]
 fn format_check() -> Result<()> {
     let context = TestContext::new_with_versions(&[]);