Detect manual re-implementations of `Ordering::then_with` and similar APIs

What it does

Clippy could detect (more) manual re-implementations of built-in functions such as Ordering::then_with. Existing lints such as manual_ok_or, manual_unwrap_or and manual_map already exist and do the same thing.

Lint Name

manual_ordering_then

Category

style, complexity

Advantage

• Helps new rust users discover new APIs
• Reduces code complexity for users that are familiar with Rust's APIs

Drawbacks

• Adding many of these patterns presumably adds complexity/runtime cost to clippy and requires developer time, so for less commonly used functions this may not be worthwhile

Example

impl Ord for SmolOffset {
    fn cmp(&self, other: &Self) -> std::cmp::Ordering {
        match self.y().cmp(&other.y()) {
            std::cmp::Ordering::Equal => self.x().cmp(&other.x()),
            x => x,
        }
    }
}

Could be written as:

impl Ord for SmolOffset {
    fn cmp(&self, other: &Self) -> std::cmp::Ordering {
        self.y()
            .cmp(&other.y())
            .then_with(|| self.x().cmp(&other.x()))
    }
}

Start by reviewing Clippy's existing manual_ok_or, manual_unwrap_or, and manual_map lints to understand how similar manual API re-implementations are detected. Define the manual_ordering_then pattern from the issue's example and verify that the lint recognizes it and recommends Ordering::then_with without changing unrelated code.