GreXXL gogog the way Formulaire is designed, only submissions tied to a Flarum model are visible on that model. There's currently no concept for a list of public submissions.
You can create a "multi-entry" field inside of a form. It's rendered like a table and can be configured to have an unlimited number of rows. However it's not well designed to contain periodically added data because all the data is always returned all at once and there's also a limit for JSON fields in MySQL which you might reach if you start having too many post-like content inside of a single submission.
When I read your original post I thought of my Cimaise extension, which allows users to create public picture albums on their profiles. The pictures have a customizable title and description. But you can't add text-only entries inside of an album.
One option that doesn't involve any of my extensions would be to implement the ability for users to create a "personal discussion", a special discussion where only the user themselves may post and that might be hidden from the list of all discussions. Posts from that discussion could be shown under a new tab of the user profile. This is something you could also do natively with Flarum, just use a custom tag for this and explain to users how they should use it. They could then link their discussion in their bio or something. Currently Formulaire doesn't allow adding fields to posts (only discussions), but this could be a feature that ties in with that personal discussion feature to add specific information to each post.