The TagManager format is not really meant to be used directly (hence the lack of docs), it's meant to be generated by Geany itself using the `-g` option. If you're really interested, you can find the code that reads and writes this format in [tm_source_file.c](https://github.com/geany/geany/blob/9c91c287803ae05ce0f2aacd605564301e0ef4aa...).
I believe Geany can also load Ctags format, written by tools like [universal-ctags](https://github.com/universal-ctags/ctags) as well, if you need something more advanced than pipe format, without reverse-engineering TM format.