We have the theme component Discourse Mermaid here on Meta rather than the plugin, and I can see a similar result using the example:
flowchart LR
subgraph "One"
a("`The **cat**
in the hat`") -- "edge label" --> b{{"`The **dog** in the hog`"}}
end
subgraph "`**Two**`"
c("`The **cat**
in the hat`") -- "`Bold **edge label**`" --> d("The dog in the hog")
end
I’m not following the linked example though, as that doesn’t appear to show the bold/italic text in the finished flowchart: (though doesn’t show the Markdown itself)
I’ll make some enquiries. 