bubble has revise the filemanager in a way that using bubble as an intermediate hop for files you can get a bubble based S3 URI that can be used in a proxy service to call the 2 api’s you mention.
If you leave aside WP for a minute taking a look here on AWS from/to proxy it should be clear that w minimal changes the proxy handles any Fetch.POST based REST api ( expects file in the request.body as a binary and readableStream format).
read here and respond if you think that adding an endpoint for WP uploads makes sense.
Parse-Server has REST upload very similar to WP and the code for that is already in the proxy
see here code
If you want a UX where user form is on a page and the user rather than your system is selecting the file having destination TO: wordpress then that would change things a bit but if you can figure out how to get the file to the bubble.S3 layer as a binary then this all works with minimal changes.