Hi,
Client-server compatibility relies on the protocol (AMQP 0.9.1 and/or other protocols that you use) and is therefore very good in general.
Upgrading RabbitMQ itself may require quite a bit of work given how far behind you are. You'll also need to also upgrade Erlang of course.
On top of that, simply upgrading the configuration you have is one thing, taking advantage of new features such as quorum queues. You can of course separate these steps and upgrade first and modernize later.
You haven't mentioned which client you use and at which version you are right now, but assuming Java, you need to pay attention to JDK compatibility and other breaking changes introduced since then. Also, similarly, new Java client provides new APIs that you may want to start using once you upgrade the library.
Lastly, assuming you use TLS, you will need to make sure that after the upgrade, the clients and servers support the same TLS version and ciphers, especially if you want to start using TLS1.3.
I see no reason to upgrade all applications at once but of course a change like this requires through planning and testing.
Lastly, there are obviously companies that offer professional services in this area - feel free to reach out if that's something you'd like to consider (I work for VMware).
Best,