does "this" pointing to the class or the object itself?

In this case, this refers to the object. No, not the JavaScript's object ({}) data type, but the instance of the price_update class when instantiated with new price_update().

Oh, right, you have a typo there (user_id1 instead of user_id in the constructor parameters). user_id was not defined there (even though the SO mods edited the question), hence undefined.

Snippet of the original post:

class price_update {


    constructor(api_key, url_endpoint, user_id1, store_name) {
        this.api_key = api_key;
        this.url_endpoint = url_endpoint;
        this.userid = user_id;
        this.store_name = store_name;
    }

    #updatePriceQuantity_parameters = {
        Action: "UpdatePriceQuantity",
        Format: "json",
        Timestamp: this.#timestamp_generate_function(),
        UserID: this.userid,
        Version: "1.0"
    };

does "this" pointing to the class or the object itself? Yes. this points to the object itself.

Why 'this.userid' is assigning undefined value? You are attempting to set the value based on a property (this.userid) before you've ever defined it (either in the constructor or anywhere else).

Instead, you will want to do something like this in your constructor:

class price_update {


    constructor(api_key, url_endpoint, user_id, store_name) {
        this.api_key = api_key;
        this.url_endpoint = url_endpoint;
        this.userid = user_id;
        this.store_name = store_name;
        this.#updatePriceQuantity_parameters.UserID = user_id;
    }

    #updatePriceQuantity_parameters = {
        Action: "UpdatePriceQuantity",
        Format: "json",
        Timestamp: this.#timestamp_generate_function(),
        UserID: '',
        Version: "1.0"
    };

Note that we're setting the value in the constructor while we're inside of the instance of the object itself. You can do it like this, or in another method if you like. Either way, you have to instantiate the object first before you and access/apply properties that you have set during construction.