PCKE implementation for React SPA and REST API

Question

I need to implement a system where the frontend is a pure SPA made with react (by pure I mean it is only hosted as a bunch of static files) and a nodejs REST API made with express. I can not use any 3rd party authentication providers like Auth0, etc. so everything must work locally.

The app must have authentication and it must be more or less up to modern standards. I am looking to implement PKCE flow with short-lived JWT auth tokens and long-lived refresh tokens.

There is one thing I am confused about. Every guide on PKCE flow always mentions redirects from one URL to another during the auth flow. In my setup, however, redirects are highly unwelcome.

I want to check and find out whether it is OK to implement PKCE flow using pure XHR requests to communicate between the SPA and API. Is it appropriate to do so? What major risks are there compared to a setup with redirects?

EDIT: to make this question more specific, what should be the PKCE authentication flow if you can only use SPA and XHR (and must avoid redirects)?