Is it good to use domain + subdomain for production website with 2 different functionalities

I am building React application and it is almost done. To use application you have to login/signup and continue. Now I am considering building website with all information about the application with standard pages - Contact, About and etc. I am thinking about making this website with WordPress (faster and already good with) and to put the application in subdomain:

mydomain.com - site

app.mydomain.com - application

Is it good practice to do that? What are the benefits and the minuses of using this method? The only minus I see is that for my SSL certificate I will have to purchase a little more expensive plan but this is not a problem. I will have a link from my website to my application (for example in menubar called "Login"). And 2 more questions:

1. Will they exist like separate sites? I think this is "yes".

2. And if the first Questions is "yes" then data transfer between them will not be performed. The only thing that will be affected is token (the website will not know if user is logged unless maybe I use storageSession for token check).