I am at 29 weeks, but my office is still assigning me new work to take charge of. Is it common?

I feel the same too, they are putting more on my plate because I'm the only one who can complete the tasks fast and efficiently (what my boss said). My mindset is baby is my priority now. It's not easy especially if you're Type A personality and want to achieve before going out on leave. Refocus on yourself. You will still get paid eventually and work will still be there. Do what you can and keep your sights on yourself happy and healthy. All the best Mummy 👍

Technically at 29 weeks, you are still supposed to work as usual and what you are tasked till your maternity leaves start. But yes, you don't have to respond during maternity leave. Just handover to your cover or your boss whatever is left before your maternity leaves start.