I had a similar requirement and ended up with
- Piwigo.org 11 Photo gallery hosted on a private web server
- Plugin https://github.com/cccraig/MugShot (I had to use the master branch which is mostly compatible with Piwigo 11) - this let's you draw rectangles and tag persons
In addition to your requirement I wanted to be able to share and collaboratively tag the data.
Concerning eternal standards / backup:
- The plugin stores the face data the MySQL Database table face_tag_positions - you can export this using PHPMyAdmin / Adminer manually on a regular basis
- You might also have to export the table
By archiving this data you might be able to reconstruct the tagging information even without constantly updating the Piwigo server.
With a bit of work it should also be possible to export this data to static HTML Files (with Imagemaps) which probably is a good format for archival. But then you loose the comfort of editing the data.