I may be wrong, but according to the Vue documentation https://vuejs.org/guide/components/events.html you don't have to use defineEmits() when calling update inline on the template area "...The $emit method that we used in the < template > isn't accessible within the section of a component, but defineEmits() returns an equivalent function that we can use instead:...".

I tested and this worked:

<script setup>
defineProps({
  modelValue: String
});
//let emit = defineEmits(['update:modelValue']);
function onTabPress(e) {
  let textarea = e.target;
  let val = textarea.value,
    start = textarea.selectionStart,
    end = textarea.selectionEnd;
  textarea.value = val.substring(0, start) + "\t" + val.substring(end);
  textarea.selectionStart = textarea.selectionEnd = start + 1;
}
</script>
<template>
  <textarea
    @keydown.tab.prevent="onTabPress"
	@keyup="$emit('update:modelValue', $event.target.value)"				
    v-text="modelValue" />
</template>

Refactor to defineProps and defineEmits