Change some APIs for downstream crate implementors

[SpriteOvO]

Currently, I'm working on a separated crate spdlog-telegram which writes log records to a Telegram chat, and I found some API is hard (even impossible) to use from a downstream crate implementor in the ecosystem.

This PR improves some APIs to solve such problems (with API breaking changes, of course), aiming not just to make crate spdlog-telegram, but more downstream crates could be easily developed in the ecosystem.

I will update more details to explain each commit changes later.

[SpriteOvO]

As a first thought, I was tried to omit the explicit ErrorHandler::new calling by accepting a generic type F where F has Into<fn> impl if user is passing a closure as a argument to {,set_}error_handler methods.

However, it doesn't work. It is surprised that there is no such an auto implementation:

fn foo(_: fn()) {}
fn bar<F: Into<fn()>>(_: F) {}

fn main() {
    foo(|| {}); // OK
    bar(|| {}); // Error
    bar::<fn()>(|| {}); // OK
}

I did ask about it on Zulip (link), it may be an opportunity to contribute to Rust stdlib.