You could use the Linking module with the mailto scheme to open the mail app.

Import the Linking module:

import { Linking } from 'react-native';

Then, use its openURL() function to open the mail app:

await Linking.openURL('mailto:youremail@example.com');

You can also use the canOpenURL() function to check if the link is supported:

const url = 'mailto:youremail@example.com';

const supported = await Linking.canOpenURL(url);

if (supported) {
  await Linking.openURL(url);
}

So, in your example, that'd look like:

import React, { useState, useCallback } from 'react';
import { View, Text, TextInput, Linking } from 'react-native';
import ModalButton from './ModalButton';

const StoreReview = (props) => {
    const [comment, setComment] = useState('');

    const emailAddress = 'youremail@example.com';
    const url = `mailto:${emailAddress}?body=${comment}`;

    const handlePress = useCallback(async () => {
        const supported = await Linking.canOpenURL(url);

        if (supported) {
            await Linking.openURL(url);
        }
    }, [url]);

    return (
        <View style={styles.container}>
            <Text style={styles.headerText}>
                We are very sorry about this.
                Can you share your experiences?
            </Text>
            <View style={styles.commentArea}>
                <TextInput
                    onChangeText={setComment}
                    value={comment}
                    multiline={true}
                />
            </View>
            <View style={styles.button}>
                <ModalButton
                    buttonText="Send"
                    onPress={handlePress}
                />
            </View>
        </View>
    );
}

export default StoreReview;

Edit: I just realized you want to include the comment in the email's body.

To set the email subject and body, simply change your URL from mailto:youremail@example.com to mailto:youremail@example.com?subject=Hello&body=World.

So, in your case, the URL should be:

const [comment, setComment] = useState('');

const emailAddress = 'youremail@example.com';
const url = `mailto:${emailAddress}?body=${comment}`;