Is there any impact on upgrading the Aurora PostgreSQL Instance class from db.r5.large to db.r6g.2xlarge

Hello.

Changing the instance class incurs downtime.
https://docs.aws.amazon.com/AmazonRDS/latest/AuroraUserGuide/Aurora.Modifying.html

If you have created a read replica of Aurora and set up a cluster, you can reduce downtime by performing failover.
However, it is highly likely that this will change depending on the environment and how Aurora is used, so we recommend that you test it once in a verification environment.
https://repost.aws/knowledge-center/aurora-mysql-downtime-factors

If your Aurora DB cluster has one or more Aurora replicas, then the replica is promoted to the primary instance during failover events. A brief downtime occurs, and read and write operations fail with an exception. Service typically restores in less than 120 seconds, and often less than 60 seconds.

To increase the availability of your DB cluster, create one or more Aurora replicas in two or more different Availability Zones (AZs). For more information, see Fault tolerance for an Aurora DB cluster.

It's probably okay, but please note that "db.r6g" cannot be used with older Aurora versions.
https://docs.aws.amazon.com/AmazonRDS/latest/AuroraUserGuide/Concepts.DBInstanceClass.html