Is there still an option for independent trekking in the Annapurna area or do you have to have a licensed guide?

Aside from the Everest region then yes, officially, you do now need an officially recognised guide to hike inside any national park/protected area in Nepal. This would include most of the main Annapurna trails.

However, enforcement of the rule in the Annapurna region has been spotty so far. There are plans (in theory at least) to start enforcing the new rule in 2024.

I would say though that a guide is just a good idea anyway because a good guide (and getting a good one is key) will enhance your trek by giving background information, offering up interesting side routes, translating when required, opening cultural doors and, of course, providing a bit more safety. Not to mention that it gives much needed jobs to local people and in the big picture it costs very little.