Java based editor jEdit allows to syntax highlight plethora of languages and their file extensions. Adding typescript highlighting can be as simple as exiting file jEdit/modes/catalog.
One can take advantage of the fact, that the typescript is an extension of the javascript, so .ts extension can be added. There is also .ts extension already for typoscript, so it needs to be disabled:
<MODE NAME="javascript" FILE="javascript.xml"
FILE_NAME_GLOB="{*.{js,ts},Buildsub}" />
<MODE NAME="typoscript" FILE="typoscript.xml"
FILE_NAME_GLOB="*.ts_disabled"/>
Better way would be to develop specific typescript.xml, which would allow to add new features.