How to include META fields in Wordpress API Post?

First of all, you need to set the 'show_in_rest' property to true and 'supports' property should include 'custom-fields' when you are registering a new post type. You need to support 'custom-fields' if you want to include the meta fields.

Note that for meta fields registered on custom post types, the post type must have custom-fields support. Otherwise, the meta fields will not appear in the REST API. https://developer.wordpress.org/rest-api/extending-the-rest-api/modifying-responses/

function cptui_register_my_cpts() {

    /**
     * Post Type: Experiences.
     */

    $labels = array(
        "name" => __( "Experiences", "twentynineteen" ),
        "singular_name" => __( "Experience", "twentynineteen" ),
    );

    $args = array(
        "label" => __( "Experiences", "twentynineteen" ),
        "labels" => $labels,
        "description" => "",
        "public" => true,
        "publicly_queryable" => true,
        "show_ui" => true,
        "delete_with_user" => false,
        "show_in_rest" => true,
        "rest_base" => "",
        "rest_controller_class" => "WP_REST_Posts_Controller",
        "has_archive" => false,
        "show_in_menu" => true,
        "show_in_nav_menus" => true,
        "exclude_from_search" => false,
        "capability_type" => "post",
        "map_meta_cap" => true,
        "hierarchical" => false,
        "rewrite" => array( "slug" => "experience", "with_front" => true ),
        "query_var" => true,
        "supports" => array( "title", "editor", "thumbnail", "custom-fields" ),
    );

    register_post_type( "experience", $args );
}

add_action( 'init', 'cptui_register_my_cpts' );

Now, you need to register the meta fields using the register_meta().

add_action( 'rest_api_init', 'register_experience_meta_fields');
function register_experience_meta_fields(){

    register_meta( 'post', 'location', array(
        'type' => 'string',
        'description' => 'event location',
        'single' => true,
        'show_in_rest' => true
    ));

    register_meta( 'post', 'date', array(
        'type' => 'string',
        'description' => 'event location',
        'single' => true,
        'show_in_rest' => true
    ));

    register_meta( 'post', 'event_url', array(
        'type' => 'string',
        'description' => 'event location',
        'single' => true,
        'show_in_rest' => true
    ));

}

Note: The meta fields must be unique. Prefix your fields in ACF to make it unique.

JSON doesn't use single quotes to wrap a string. It uses double quotes. You are sending invalid JSON.

Now, if you want to create a experince post type. Use a JSON linter to validate your json. https://jsonlint.com/

Make a POST request to http://paathsala-plugin.test/wp-json/wp/v2/experience, with the fields

{
    "title": "test",
    "content": "testingfrompython",
    "status": "draft",
    "author": 1,
    "meta": {
        "location": "NYC",
        "date": "never",
        "event_url": "http: //google.com"
    },
    "featured_media": 1221
}

WordPress doesn't allow you create resource directly. You need to authenticate your REST request. I am using the Basic Auth for authenticating WordPress REST API. You need to install a plugin. Grab it from here: https://github.com/WP-API/Basic-Auth

I have tested the following python code.

import base64
import json
import requests;

# Data to be send
data = {
    "title": "test",
    "content": "testingfrompython",
    "status": "draft",
    "author": 1,
    "meta": {
        "location": "NYC",
        "date": "never",
        "event_url": "http: //google.com"
    },
    "featured_media": 1221
}

# I am using basic auth plugin to for WP API authenticaiton
username = 'admin'
password = 'blood9807'

# Encode the username and password using base64
creds = base64.b64encode(username + ':' + password)

# Create headers to be send
headers = {
    'Authorization': 'Basic ' + creds,
    'Content-type': 'application/json', 
    'Accept': 'text/plain'
}

# Convert the python dictionary to JSON
data_json = json.dumps(data)

# Create a post
r = requests.post('http://paathsala-plugin.test/wp-json/wp/v2/experience', data = data_json, headers = headers )

print(r)

@Peter Foti can you try below function for add meta value in your API.

add_post_meta( <value>, <name>, $meta_value ,true );

For Reference see this Link