Generally, when an app requires data, what's required is having an API in that App that allows listening to certain input (and eventually then do certain actions).
This is what the Toolset Forms API does.
It allows to listen to certain input, and manipulate it at a given moment, then do a certain action with it, related to what it does (create posts and users) in the range of PHHP possibility.
Hence, the place you look for such an API is the mailwizz app, because it is the one that will manipulate, or else use, the data it reads from whatever object you pass to it.
This is basically the same as I already explained in the ticket you read about:
https://toolset.com/forums/topic/sending-cred-data-to-third-party-systems/
I understand the issue you face now, you don't know how to write the code that gets the $name $email and ... so on, to put it in a Forms API Snippet so that it can be sent it back to the api of mailwizz.
The problem here is, as I try to explain in the previous ticket and above, that the approach to the solution is wrong.
You would have to look out for an API in the plugin that will work with it.
Then you don't need to "send" that data anywhere, you just need to "listen" with the 3rd Party APP to the right endpoints as provided by that API.
If there is no such API in that software it will be very difficult passing data to it with any tool you choose.
See, the Forms API is really nothing else but a set of "moments", taken from the standard life of a post-publication process in WordPress.
You have save_post() in the backend, from WordPress, and Toolset Forms uses the same.
it, however, offers a few moments in that process where you can hook in and add whatever code you want.
That's like you'd add any code you want to the save_post() hook of WordPress
If you can pass that data in the save_post() hook to your third party, it'll be possible in Forms. However, both the save_post and forms API will need to send the data to things provided by the third-party app.
If those endpoints are not there, no code will be able to send any data to it.
What I can definitely help with here, is to "get" the data in a Forms Hook itself, when you submit a Form. You can later do anything you want with it, if PHP's limitations and WordPress limitations allow it.
Usually, you will get data from the form using the $_POST['form_field_name'].
You can get the precise form_field_name from the HTML source of the Form when analysing it in the front end.
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I suggest to var_dump or error_log(print_r($var_to_dump, true)); the $_POST so to see what you actually have at disposition.
Note, sometimes you will need earlier or later Toolset Forms hooks or instead of $_POST use post object of $post_id, to get Fields and Post data:
https://toolset.com/errata/cred_save_data-does-not-hold-native-post-data-in-post/
From here on, you have the data and can do with it what you want - within the Forms Hook moment you are (cred_save or any other hook) and within WP's and PHP's limitations.
So if at this moment an API hook of a third party can be fired, and needs above data to be populated, you can use the variables populated with the $_POST data or $post_id's object (get_post($post_id))
See: https://developer.wordpress.org/reference/functions/get_post/
Here is an example that gets your_custom_field_slug value and updates the post title with it:
https://pastebin.com/2BTbVbcs
Now, this is the exact same you'd do when updating or firing any 3rd party API with that data, just that instead of wp_update_post() you'd fire your 3rd party's API method at this point.