Version 7 of MCMCChains has a very minor breaking change: it just redefines the display of a chain, so that no summary information is shown anymore. Therefore, this version actually works without issues with Pigeons.
https://github.com/TuringLang/MCMCChains.jl/releases
I propose therefore to change the compat entry for MCMCChains into
MCMCChains = "6", "7"