There are 2 (or rather 3) 'flavours' of Flyspray.
Which one you use is decided at installation. Once you started really using Flyspray stick to the one choosen.
After installation, you find this setting in the flyspray.conf.php :
syntax_plugin = "dokuwiki" ; dokuwiki, none, or html
- 'none'
- 'dokuwiki' syntax is the image you posted. It is using a simple textarea with a simple toolbar.
and
- 'html' is using CKEditor4 with a choosen set of CKEditor4 plugins that match nearly the same features as the dokuwiki plugins. This is the image that is still in the documentation. Nobody has updated that there are several text editing UIs.
Due to the difference in the backend, the 'html' is not compatible with the others. And so there is also no toggle in the UI to switch between!
It all has historical reasons without going into detail in this short anwser here.
If you are unsure what to choose, I suggest using the 'dokuwiki' 'flavour'.
> The biggest thing I'm needing is the ability to display images inline within comments without having to explicitly create attachments, i.e. the ability to display externally linked images.
This was once able to do with the dokuwiki plugin, but was deactivated due security issue.
What I have done for myself for convenience, but not yet in the official github is showing attachments (only if they are web images) in the task and comment text. (after text bodies)