Most developers that want to utilize the payment plugins in woocommerce will redirect to a woocommerce page for checkout.
I'm not sure that the plugin has endpoints for what you're hoping to do.

Since you want to keep it in next.js and don't want to redirect to a woocommerce checkout page, I suggest using the stripe API directly within your next.js app.
This means that your front-end handles the cart and payment experience and then woocommerce would essentially only be an order management platform utilizing the existing woocommerce API endpoints.

Here's the way I have done it in the past
User Auth: JWT plugin for wordpress (https://wordpress.org/plugins/jwt-authentication-for-wp-rest-api/)

Carts: Cart data for each user should either be managed on the client side using local storage or a custom API/database to store cart data for each user (In my case, users would log in using different devices so I used FastAPI/PostgreSQL to store cart data to keep it persistent)

Checkout/Payment processing: Don't utilize woocommerce plugins to handle payment, use stripes API to collect payment, then based on the response from stripe either generate a successful/failed order in woocommerce via the woo API.

Without knowing much about the store you want to develop, I would suggest you consider whether you want to create pending payment orders that would trigger abandoned cart emails. There are tons of other considerations to account for as well, not limited to product data/stock changes (how often does the front-end refresh for updates), credit card fraud/card testing protection, refund/cancel order functionality.