This issue seems to be exclusive to variable subscriptions (probably product too). The checkout page will eventually load after 2-3mins of waiting. If I disable your plugin it loads in 1-3 seconds.
I have a feeling something weird is happening in the background, like an attempt to calculate rates for EVERY variation. Whatever it is, it doesn’t seem to happen with simple products or simple subscriptions.
I can get you setup on staging, send screen recordings or whatever else might be helpful for you to replicate and fix this bug.
These should be the relevant versions:
Multi-Carrier ShipStation Shipping for WooCommerce – Version 1.4.8
WooCommerce – ShipStation Integration – Version 4.3.3
WooCommerce Subscriptions – Version 5.0.0
WooCommerce – Version 7.5.1
WordPress v6.2