I don't feel like this is enough information to give any proper advice, it depends most on factors you haven't outlined.
What is the main reason they're keeping you on, do you think? Are they not paying attention and not accounting for costs, or are they interested in reserving your time and having you owe them some hard work as soon as it's there?
What is your mean reason for staying at this particular company, aside from getting paid to work on pet projects? Are they smart, honest, good people that you're learning from, or is it a paycheck and nothing more?
Have you reached out to your manager and asked for a project repeatedly? Do you have co-workers you can help, even if you're not asked to? What is your main fear, will doing nothing for the company lead to no promotions or less pay or a bad reputation? Will there be repercussions for future jobs if you keep going with this one, or can you get another job easily regardless of what this company thinks about you?
Does getting paid to work on your pet project have more value than working for the company? It's a pretty good deal for you if they don't care about paying for your downtime.
Last time I was in a similar situation, I spent my time doing research and programming competitions. My employer was okay with it, work eventually picked up again and I didn't lose any status in the organization. In the mean time I got to learn a lot, and travel to Spain to present my paper. I had a blast, and I super appreciated the opportunity to explore. I told my employer that, and I worked hard once work picked up, so I walked away with nothing but a positive experience. I was also really lucky.