Limited by IOPS is a different thing than needing more IOPS. The latter is more of an organizational needs thing, are the applications using this database performing adequately? Interactive response latency, batch jobs completing on time.
However, an upgrade at a lower cost is an easy win, sure. Their cost structure is a black box, so don't worry too much about what makes this price possible. Presumably, microtransactions on IOPS is revenue from people who want more out of smaller volumes.
Cost per "provisioned IOPS" on gp3 seems to mean you pay for the quota you set. As in a static per month charge, I think. Do not expect it to burst above this quota, that's the incentive to get you to pay more. 12,000 IOPS and 500 MiBps free (and your total cost number) seems to imply 4 disks, if you want to do it that way sure. Watch costs and performance to be sure of no surprises.
As usual for storage migration, before doing so test your backup restore process. Out of an abundance of caution, even for non-disruptive changes. A good excuse to catch up on this last line defense for business continuity, if you have not done so in a while.
A storage migration would be an opportunity to check how the data volumes are labeled. Use specific identifiers like file system UUID or LVM names. Not generic block device like /dev/sdb which will eventually change. Less of your concern if using a managed database.