I have checked the source of Pkg.jl. There are two places in the code where the @info message could be emitted. Both of them check whether the registry name is "General" (obviously true in my case), and whether ENV has the key "JULIA_PKG_GEN_REG_FMT_CHECK", defaulting to true if it doesn’t.
Since that key doesn’t exist in my environment, both tests pass and the message is emitted. I don’t know when the variable for the second test could/should have been set, but I have now added
ENV["JULIA_PKG_GEN_REG_FMT_CHECK"] = "0"
to ~/.julia/startup.jl and did
pkg> registry rm General; registry add General
The message has disappeared.
Your replies prompted me to do a proper investigation, so thanks again.