How can we highlight code syntax in Frame Maker?

What code editor application is presenting that colorized code view?

Can it export to PDF*, preserving that text decoration?
If so, a quick solution is to do that, and import the PDF(s). This would preserve it as selectable text in the FM output to print or PDF (but not to XML or HTML), whereas doing it with screenshots would have it be raster pixels in all workflows.

*Can it export to HTML, preserving the markup?

You could definitely create a series of Find/Replace steps with regular expressions to apply character formats to different keywords.

There are some batch find/replace add-ons. E.g.:

FindReplace from Klaus Göbel

https://4xscripts.com/en/scripts

FindChangeBatch from Rick Quatro.

I do not know, if they can also replace with a character format.

Not that I know of - you should create your own code_green, code_blue, code_bluebold paragraph tags to apply to the text OR just bring it in as an image.