I changed the storage type of a RDS instance from gp2 to provisioned IOPS after running out of IO Credit. Do I have to wait to finish the Burst duration?

I have addressed your concerns as follows-

Please allow me to mention that, after changing the storage type of a RDS instance from gp2 to provisioned IOPs and running out of IO credit, there is no requirement to wait for the burst balance to revive or burst duration to complete.

Regarding your second query, if we consider "unlimited mode" in db.t3 instance classes, in the scenarios when the CPU utilization goes above the "Baseline CPU utilization" threshold value, even after exhausting all CPU credits, it will continue to burst above the baseline and it will not throttle. As you might be aware, you will be charged an additional cost per CPU per hour for the same. Kindly refer to the following doc for the related costs-

[+] Amazon Aurora Pricing - https://aws.amazon.com/rds/aurora/pricing/?pg=pr&loc=1