It’s not easy to answer on that, as think you trying to do something that you are not fully aware from a technical point of view (sorry).
Are you transferring hosting or domain, as this is two different aspects?
If you transferring hosting than you need to transfer files and database to new hosting and set everything. If you transferring domain only, you just need to confirm that DNS is pointing to the server when you got the site hosted.
I am only transferring the domain. So technically my WordPress website does not have a domain anymore, since it leads to my Squarespace website now. What I am now wondering is how I can access my WP website now that it does not have an assigned domain anymore.
I think you mixing something and we need to clear this thing up.
1. Domain is an address that ponting to server
2. Server is a place where website is places
If you have Domain and Server with Bluehost, when you move to Squarespace than you move both?
Have you got still access to your panel at Bluehost? though FTP and database though phpmyadmin etc? (not quite sure how they work, as not used them).
You shall copy all data through FTP and export your database before moving to Squarespace and than at Squarespace upload files and import database. Than point through domain DNS to direct to Squarespace server.
I am well aware of all this. However, I am setting up a complete new website on SS from scratch, and am moving that domain to that new website.
I just want to know what happens to my WP website once it doesn’t have a domain assigned anymore.
Ok, no problem.
The website cannot exist without a domain. You cannot access the website when there is no domain attached to it (though options).
If you moving website domain living old site intact, just change the main domain for a website to a subdomain or something that will point to a place where currently website is placed.
You can do this through SQL wp_options (first two options) or through Dashboard > Settings > General.
Once your old website will work under the temporary domain, you can move the other that you changed from.
