I'm currently in the middle of a billing cycle. If I change the monthly plan to a yearly plan at this point, will it reflect on the next billing cycle?

According the Shopify, if you switch to the yearly plan, the plan will take effect immediately and you will be prorated on the next cycle

https://help.shopify.com/en/manual/your-account/manage-billing/your-invoice/apps#app-prorating-upgrades-and-downgrades

However, note that Shopify has a billing threshold

https://help.shopify.com/en/manual/your-account/manage-billing/your-invoice/invoice-overview#about-billing-thresholds

If the subscription goes above that threshold you might get a 2nd charge this cycle.