The hydroponics forum might be able to better help with this, and I know nothing about hydroponics.

...But I would assume that the roots sitting in water is not a good thing for maintaining a plant long-term. Looking at the product's intended design, if you have the "wicks" in there too, then it should probably rely solely on those for water, so I would suggest trimming back any roots that touch the water. You should also replace the water every now and then to ensure that it doesn't stagnate.

I would also assume that some soluble fertiliser in the water once or twice might help, given the small amount of soil. Do the instructions mention anything about that?

Growing in hydroponics, the plant needs water, air, and nutrients. Did that system come with some nutrients? If not, you should buy some liquid nutrients and add it directly to the water. It's okay that the roots are sitting directly in the water because that's how a deep water culture system works, although the water needs aerated. I would put more water in the system with a straw sticking out so you can blow air into the water, but I'm a noob to this, so like Sophie said, a hydroponic forum would provide better answers.

Thanks for your replies! I will post in the Hydroponics forum and see what they say as well. In the meantime, I have trimmed the roots so that they aren't so deep in the water, changed the water, and added plant food to it. Too early to tell whether that did anything!

First, you need to paint your glass jar with chalked paint spray to protect your roots from algae to grow. You are doing a Kratky method which is my favorite. If you roots are getting longer, then you can cut them carefully with sharp and sterilized scissors 1/3 from the bottom after washed them thoroughly.

Here's how to trim your roots.

https://createyoutube.com/fb/Ryhvwdy4yLE