overload for emittable events

[michaelcozzolino]

I have the following component

<template>
    <div>
        <input :label="label"
                    :name="name"
                    type="number"
                    :step="step"
                    :disabled="disabled"
                    v-model="editableInput"
                    :min="min"
        />
    </div>

</template>

<script setup lang="ts">
import { computed }   from 'vue';

interface Props {
    label:       string;
    name:        string;
    step?:       number;
    disabled?:   boolean;
    min?:        number;
}

withDefaults(defineProps<Props>(), {
    step: 0.01,
});

defineEmits<{
    (e: 'update:modelValue', modelValue: string | null): void;
    (e: 'update:modelValue', modelValue: string): void;
}>();

const [input, modifiers] = defineModel<string | (string | null), 'null'>({
    required: true,
    set:      (value: string | (string | null)) => {
        if (modifiers.null) {
            return Number(value) === 0 ? null : value;
        }

        return value;
    },
});

const editableInput = computed({
    get: () => Number(input.value),
    set: (newInput: number) => input.value = `${newInput}`,
});
</script>

The goal of this component is to have a stringable number and allow a nullable value in case we have 0 when the null modifier is specified. The v-model with the current vuejs features emits an event with the following signature
(e: 'update:modelValue', modelValue: string | null): void;

but it does not take into account the modifier, so I would like to have different emit function signature depending on the modifier whenever it is required. It means having sort of overloads for the defineEmits, that in case of the v-model could be specified in the defineModel template or manually in the emits such as

defineEmits<{
    (e: 'update:modelValue', modelValue: string | null): void; // with null modifier
    (e: 'update:modelValue', modelValue: string): void; // without null modifier
}>();

UPDATE:
actually it seems, this is possible by using a generic component
<script setup lang="ts" generic="T extends string | (string | null)">

but I'm not sure it is the right way to do it