Question about subdomain SEO, Squarespace x Next.js

SEO Beginner.

I have a client with an existing Squarespace site and they've tasked us with building an improved user experience for displaying some information they have on a CMS.

We've built a Next.js application for their improved UI, and essentially we want the application to feel like it's a part of their Squarespace site (we've mimicked their branding etc...).

The solution we've thought of is to host our Next.js application on a subdomain and have the Squarespace & Next application just link to each other.

I'm wondering about important SEO considerations that I should be thinking of with regards to this solution. Any advice/pointers/critiques are welcome.

THANK YOU