This sounds like a great use of Softr and Airtable and you can achieve all you have described using both platforms working together.
You could set up an admin (group) in Softr and give visibility of a Softr form to this group on a page they also have visibility of. Collect user details via this form to add to Airtable. Create an automation in Airtable triggered by new users being added and call on Zapier to create users in Softr and generate Magic Links for them that are sent back to your Airtable users table.
For data entered by users, use a single table for all. Ensure that one of the fields (it can be a hidden field) has an identifier to allow for data to be filtered by parameters you set (these are the conditions you add to dynamic (list) blocks). For example, for a user to only see data they enter, have Softr filter by logged-in user (their email or Magic Link is my method). If you want to display data to all users from the same company, filter by (a field) Company Name and ensure that Company Name is captured when users enter any data using your form.
I hope you enjoy learning how to make this work for you and seeing successful results.