The bad news is that it doesn't work too. I have added it, closed geany, reopen and all is the same.
<details> <summary>WFM, looks like that:</summary>
Default: 
Adding `lexer.bash.styling.inside.string=1` 
Adding `lexer.bash.styling.inside.backticks=1` 
Adding `lexer.bash.styling.inside.heredoc=1`  </details>
One question: what is the correct: altering via Geany Tools, ... or editing directly in the file /usr/share/geany/file...
Because opening in Tools, all lines appear commented and is is different from the same file in /usr/share/geany/file... What is actually used ?
Both are used together. If something is not defined in the user's configuration, the value is looked up in the /usr/share one (or whatever the Geany installation path is).
All you need to do is go through Tools… and replace the whole content with literally what I mentioned above. Or add it (uncommented) somewhere.