You should be able to just copy and edit the XML definition file (html.xml); as long as you don't need stuff beyond the basics, like code-folding, advanced coloring based off of case-handling blocks or multiple conditionals, separate formatting for lead characters, label coloring, xml-based commenting, language mixing (coloring of embedded scripts), support for coloring of duck-types, etc. If you need anything "advanced" you need to write your own lexer, in which case most of the below applies.
Even still, the templates I listed below should give you a head-start on your own language definition file.
As far as I'm aware, Notepad++ uses Scintilla Lexers for determining its code rules.
You'll have to create your own lexer, but...the HTML Scintilla Lexer is already included in the Scintilla source code.
Then you would insert your custom lexer using a plug-in, like Gary's Lua Highlighter Plugin.
Resources for building a custom lexer:
That being said, Geany is very similar to Notepad++ (based off the same engine, Scintilla), so you might want to see whether it's already been done for Geany, or whether there's an open-source project for it in the works. This would at least give you a head start.
If that doesn't help, there are IDEs and editors with Twig support built-in, like:
GEdit has published their XML definition of the language here, which might help as a reference when creating your own definition file or lexer; there's also another template published by the guys from Twig here that might be of some help.
Here are the best Notepad++-specific tutorials for creating custom lexer's/User Defined Languages I can find:
If you want to get brave and build your own Scintilla dll, reference these threads, to see a guy who got it working, and to show up in the language list (use the previous/next thread message to see responses, or the thread index; it's a mailing list, so its UI isn't the best)
Hope that helps or gets you at least more of a head start!
Best Answer
Notepad++ provides 2 types of features:
Based on what you write, it seems what you want is auto-completion on function only + suggestion on arguments.
To do that, you just need to change a setting.
Settings
>Preferences...
>Auto-completion
Enable Auto-completion on each input
Function completion
and notWord completion
Function parameter hint on input
(if you have this option)On version 6.5.5 of Notepad++, I have this setting
Some documentation about auto-completion is available in Notepad++ Wiki.