Thanks to covid-19, we are in a lockdown, and no one knows how long it will last....I'm doing experimental science, but the lab is shut down....I'm feeling so anxious because apparently I have nothing to do! I can do no more experiment, and I've already analysed all the data from my old experiments.

My supervisor just tells me to write a chapter for my thesis. But doing the writing full-time is boring, so I hope I can do something else. Also, there'll be a 6-month period at the end of my PhD for writing the thesis, so I don't really need to work hard on it now. I have plenty of time now, but have nothing more meaningful to do.

I've heard another PhD student in my cohort has been assigned a side project by his supervisor for the lockdown period. I think that's a good idea. But when I asked my supervisor for a side project, he was like 'What side project? You don't need one. I'm sure you'll have enough data by the end for your thesis.' I didn't know what to say, but felt very disappointed. I emailed a postdoc, who's working in the same group as me, about how bored and anxious I'm feeling. I thought he would understand my feelings cos we share the same supervisor and do similar experiments. To my surprise, he didn't reply. But today I heard from someone else that my supervisor gave the postdoc a side project and he's busy working on it! You know how frustrated I'm feeling now! I'm even feeling angry. I've already written an email expressing my anger, but I'm hesitating whether I should send it to my supervisor right away!

Its understandable to feel how you do. Being a scientist and being away from the lab can be testing. In my research group, everyone has been task with thesis writing (Students) and postdocs(me) have been told to write papers.
I know it hard to write full time, but that is what you'll have to do in the last 6 months. I would imagine it would be better to write what you can now, just in case you need those final months to do experimental work.
In term of I have" nothing to do", can you make some graphical abstract, create imagines or double-check all the references you have used to date? Can you take any courses online, such as an R stats course etc? It doesn't all have to be about writing.
In terms of a side project, I personally wouldn't want one, this will distract from your thesis, and may not be useful towards your PhD.
I would thread lightly about sending an email to your supervisor about how angry you are. You don't want to upset a relationship. Also, see it from their side, s/he more than likely has PhD students, post-docs and classes that are now being done online, plus exams are coming up, s/he could be quite stressed. I would, however, ask if possible for a video call/meeting to discuss what exactly s/he would like to see from you during this time. Sometimes having smaller goals to work to can be helpful.

+1 with Nead - delete that email if it's anything like your post. It will only make you sound like you're not prepared to do the work for your thesis that you've been asked to do. Let's face it, if we're lucky enough just to be bored and frustrated right now, then we're the fortunate ones who aren't dealing with illness and bereavement.

People are being affected differently by COVID-19 and have to respond differently. So don't compare yourself to other student who may be affected differently to you. There is no point doing a side project unless it benefits you in the long term and you can finish it. If you start something irrelevant to your PhD and don't finish it during your lockdown you may just waste your time. As when the labs reopen, you will be super busy and not have time for side projects. So if there isn't a side project that that is both relevant to you and smallish you might as well lie on the sofa. Working on your thesis now is useful as you can use the 6 months at the end of your PhD to do more lab work.

I have started too many side projects that I haven't finished. I would do the first few experiments and then find that the project requires soo much work than I initially intended. My preliminary data would not be enough for a paper and so irrelevant to my main work that it is now useless. It is easy to start a side project but difficult to "finish" it.