"Slave" has been deprecated in favor of "agent" since Jenkins 2.

This is outside my area of expertise, but the Git plugin (possibly others) extend the class core/src/main/java/jenkins/security/MasterToSlaveCallable.java

This means it would be pointless to rename the extending classes until this is renamed in core.

What are the compatibility issues, and has there been discussion on them? What it would it take: some coordinated effort on each affected plugin?

For a real world workflow where someone contributes to FOSS projects and encounters this:

1. I reviewed a pull request on a FOSS project, and saw a Jenkins job was failing
2. Viewed console output to identify the issue (here, a benign one, the author likely force-pushed while the job was running), and read this:

3. Caused: hudson.plugins.git.GitException: Could not checkout 1e45d6cd7e5d6b076293b442a9ad14bcb3ba3f94
   at org.jenkinsci.plugins.gitclient.CliGitAPIImpl$9.execute(CliGitAPIImpl.java:2777)
   at org.jenkinsci.plugins.gitclient.RemoteGitImpl$CommandInvocationHandler$GitCommandMasterToSlaveCallable.call(RemoteGitImpl.java:161)
   at org.jenkinsci.plugins.gitclient.RemoteGitImpl$CommandInvocationHandler$GitCommandMasterToSlaveCallable.call(RemoteGitImpl.java:154)