How can I send an Email through Website Contact Form - google-cloud-functions

Question

I am implementing a contact form on a website with Flutter web.
To make this form functional, I need to send it as an email to a recipient.
I am not even aware of what I should search for to implement this. What are the different implementation options for this case?
If I use Firebase for hosting, I could probably use a callable cloud function. Would this make any sense?
This is a pretty generic form that I implemented:
class ContactMe extends StatefulWidget {
const ContactMe({Key key}) : super(key: key);
#override
_ContactMeState createState() => _ContactMeState();
}
class _ContactMeState extends State<ContactMe> {
final _formKey = GlobalKey<FormState>();
String _name;
String _email;
String _message;
#override
Widget build(BuildContext context) {
return Scaffold(
body: Container(
padding: const EdgeInsets.all(15),
margin: const EdgeInsets.only(top: 15),
child: Column(
children: [
Align(
alignment: Alignment.centerLeft,
child: const _BrandName(),
),
Container(
padding: const EdgeInsets.all(55),
child: Form(
key: _formKey,
child: Column(
children: [
TextFormField(
decoration: InputDecoration(
helperText: 'Please enter name',
hintText: 'Darth Vader'),
cursorColor: kDarkBlue,
onChanged: (value) {
_name = value;
_formKey.currentState.validate();
},
validator: (value) {
if (value.isEmpty) {
return 'Please enter valid name';
}
return null;
},
),
TextFormField(
decoration: InputDecoration(
helperText: 'Please enter email',
hintText: 'darth.vader#star.com'),
cursorColor: kDarkBlue,
onChanged: (value) {
_email = value;
_formKey.currentState.validate();
},
validator: (value) {
if (value.isEmpty) {
return 'Please enter valid email';
}
if (!RegExp(
r"[a-z0-9!#$%&'*+/=?^_`{|}~-]+(?:\.[a-z0-9!#$%&'*+/=?^_`{|}~-]+)*#(?:[a-z0-9](?:[a-z0-9-]*[a-z0-9])?\.)+[a-z0-9](?:[a-z0-9-]*[a-z0-9])?")
.hasMatch(value)) {
return 'Please enter a valid email';
}
return null;
},
),
TextFormField(
decoration: InputDecoration(
helperText: 'Please enter subject',
hintText: 'Optimizing Lightsaber Production'),
cursorColor: kDarkBlue,
onChanged: (value) {
_name = value;
_formKey.currentState.validate();
},
validator: (value) {
if (value.isEmpty) {
return 'Please enter a valid subject';
}
return null;
},
),
TextFormField(
maxLines: 14,
cursorColor: kDarkBlue,
decoration: InputDecoration(
helperText: 'Please enter message',
),
onChanged: (value) {
_message = value;
_formKey.currentState.validate();
},
validator: (value) {
if (value.isEmpty) {
return 'Please enter a message';
}
return null;
},
)
],
),
),
),
ElevatedButton(
style: ElevatedButton.styleFrom(primary: kBrightGreen),
onPressed: () {
if (_formKey.currentState.validate()) {
//todo: add here functionalitty
//todo: Show a Succesful send message, then transfer to primary
Navigator.pushNamed(context, kScreenPrimary);
}
},
child: Text(
'Submit',
style: kTitleStyle,
),
)
],
),
),
);
}
}
P.S. I am using Flutter: 1.23.0-18.1.pre master channel.