You can provide your manual implementation of DioxusWebComponent and call register_dioxus_web_component to register your web component.

The key point is to use a Shared element in the dioxus context.

For example, the greeting example could be written with

use dioxus::prelude::*;
use dioxus_web_component::{
    register_dioxus_web_component, DioxusWebComponent, InjectedStyle, Message, Property, Shared,
};
use wasm_bindgen::prelude::*;

/// Install (register) the web component
///
/// # Errors
///
/// Registering the web-component may fail
#[wasm_bindgen(start)]
pub fn register() -> Result<(), JsValue> {
    register_greetings();
    Ok(())
}

#[component]
fn Greetings(name: String) -> Element {
    rsx! { p { "Hello {name}!" } }
}


fn register_greetings() {
    let properties = vec![Property::new("name", false)];
    let style = InjectedStyle::css(include_str!("./style.css"));
    register_dioxus_web_component(
        "plop-greeting",
        vec!["name".to_string()],
        properties,
        style,
        greetings_builder,
    );
}

#[derive(Clone, Copy)]
struct GreetingsWebComponent {
    name: Signal<String>,
}

impl DioxusWebComponent for GreetingsWebComponent {
    fn set_attribute(&mut self, attribute: &str, value: Option<String>) {
        match attribute {
            "name" => {
                let new_value = value.and_then(|attr| attr.parse().ok()).unwrap_or_default();
                self.name.set(new_value);
            }
            _ => {
                // nop
            }
        }
    }

    fn set_property(&mut self, property: &str, value: JsValue) {
        match property {
            // we allow to set the name as a property
            "name" => {
                if let Ok(new_value) = Ok(value).and_then(|value| value.try_into()) {
                    self.name.set(new_value);
                }
            }
            _ => {
                // nop
            }
        }
    }

    fn get_property(&mut self, property: &str) -> JsValue {
        match property {
            // we allow to get the name as a property
            "name" => Ok(self.name.read().clone())
                .and_then(|value| value.try_into())
                .unwrap_or(::wasm_bindgen::JsValue::NULL),
            _ => JsValue::undefined(),
        }
    }
}

fn greetings_builder() -> Element {
    let mut wc = use_context::<Shared>();
    let name = use_signal(String::new);
    let mut greetings = GreetingsWebComponent { name };
    let corountine = use_coroutine::<Message, _, _>(move |mut rx| async move {
        use dioxus_web_component::StreamExt;
        while let Some(msg) = rx.next().await {
            greetings.handle_message(msg);
        }
    });

    use_effect(move || {
        wc.set_tx(corountine.tx());
    });

    rsx! {
        Greetings {
            name
        }
    }
}

The counter example looks like this:

use dioxus::prelude::*;
use dioxus_web_component::{
    custom_event_handler, register_dioxus_web_component, CustomEventOptions, DioxusWebComponent,
};
use dioxus_web_component::{InjectedStyle, Message, Property, Shared};
use wasm_bindgen::prelude::*;

/// Install (register) the web component
///
/// # Errors
///
/// Registering the web-component may fail
#[wasm_bindgen(start)]
pub fn register() -> Result<(), JsValue> {
    // The register counter is generated by the `#[web_component(...)]` macro
    register_counter();
    Ok(())
}

/// The Dioxus component
#[component]
fn Counter(label: String, on_count: EventHandler<i32>) -> Element {
    let mut counter = use_signal(|| 0);

    rsx! {
        span { "{label}" }
        button {
            onclick: move |_| {
                counter += 1;
                on_count(counter());
            },
            "+"
        }
        output { "{counter}" }
    }
}

fn register_counter() {
    let properties = vec![Property::new("label", false)];
    let style = InjectedStyle::stylesheet("./style.css");
    register_dioxus_web_component("plop-counter", vec![], properties, style, counter_builder);
}

#[derive(Clone, Copy)]
#[allow(dead_code)]
struct CounterWebComponent {
    label: Signal<String>,
    on_count: EventHandler<i32>,
}

impl DioxusWebComponent for CounterWebComponent {
    #[allow(clippy::single_match_else)]
    fn set_property(&mut self, property: &str, value: JsValue) {
        match property {
            "label" => {
                let new_value = String::(value).unwrap_throw();
                self.label.set(new_value);
            }
            _ => {
                // nop
            }
        }
    }

    #[allow(clippy::single_match_else)]
    fn get_property(&mut self, property: &str) -> JsValue {
        match property {
            "label" => {
                let value = self.label.read().clone();
                value.into()
            }
            _ => JsValue::undefined(),
        }
    }
}

fn counter_builder() -> Element {
    let mut wc = use_context::<Shared>();
    let label = use_signal(String::new);
    let on_count = custom_event_handler(wc.event_target(), "count", CustomEventOptions::default());

    let mut counter = CounterWebComponent { label, on_count };
    let corountine = use_coroutine::<Message, _, _>(move |mut rx| async move {
        use dioxus_web_component::StreamExt;
        while let Some(msg) = rx.next().await {
            counter.handle_message(msg);
        }
    });

    use_effect(move || {
        wc.set_tx(corountine.tx());
    });

    rsx! {
        Counter {
            label,
            on_count
        }
    }
}