graphingpaper
"Does rooting compromise GrapheneOS's security?"
Its not considered GrapheneOS once you root it, devs don't support it, its not really doable without a lot of work. Also will disable verified boot unless you make your own signing key and sign your own updates
"If I root, what would be the Graphene team's recommended program(s) for recording both input and output"
GrapheneOS cannot, because you shouldn't root regardless
(Not a dev, but I seen them say this 50x now on this forum. They will probably comment on this thread if they see it saying the same thing)