So basically you are wanting somebody to write the needed code for you 
As you have already stated that you need to be using the updateContact function through the backend for updating Contacts labels.
https://www.wix.com/corvid/reference/wix-crm-backend.html#updateContact
So you just need to write your code in a backend file for this and there is a clear example in the Wix API reference for it.
Then just make sure that you import the function from the backend on your page along with your other imports and call this function in your code too.
You can read how to do this on the page that Anastasiia linked for you in her reply. Corvid Web Modules: Calling Server-Side Code from the Front-End
Examples
Update an existing contact
This example contains a backend function that updates a contact.
import wixCrm from 'wix-crm-backend';
export function myBackendFunction(contactId, firstName, lastName, email, phone) {
wixCrm.updateContact(contactId, {
"firstName": firstName,
"lastName": lastName,
"emails": [email],
"phones": [phone]
} )
.then( () => {
// contact has been updated
} )
.catch( (err) => {
// there was an error updating the contact
} );
}
You can see from this example how to add a field that is an array and as you are wanting to update the label, then you just need to add it to suit.
As shown in the Contact Info section.
ContactInfo
An object that contains information about a site contact.
Syntax
type ContactInfo = {
firstName: string
lastName: string
picture: string
emails: Array
loginEmail: string
phones: Array
labels: Array
language: string
LABELS - Array
List of contact’s labels. Labels are used to organize contacts. When setting the labels property, you can only list labels that already exist in your site’s Contacts List.