SQL Server Assembly on Failover cluster after Framework update
Are you saying that the one assembly you have references unsupported .NET framework libraries that get imported implicitly when creating your assembly? In which case it would make sense that a Framework update could have this effect. SQLCLR requires that assemblies used in SQL Server that are also in the main OS GAC be the exact same version, and the version in the main GAC is now newer on the secondary due to the Framework update.

As far as I can tell, you will need to apply the same Framework update to the primary, reload the custom assembly, and failover, and then reload the assembly again. Even if the secondary was not read-only and you were able to update the assembly, if that instance failed over to the main node (assuming it still has not received the Framework update), then the SQLCLR object(s) would again fail due to the library version mismatch. And, even right now, if the primary instance fails over to the other node, the SQLCLR object(s) will error due to the library version mismatch.