You have all (most of) the rights of an EU citizen, but you would need to discuss this with your local tax office, in whatever country you have taken up residence. It would be inadvisable to use any site such as Upwork to work under the radar without declaring tax on your earnings - this could jeopardize any rights you have to stay and work in the EU. What you do outside your normal working hours should be your business, but if picking up the odd gig on Upwork conflicts with your actual job, you could have problems.
Also, your picture does not conform to Upwork's ToS.
Please follow the advice Nichola shared regarding contacting a tax advisor. Also, upload a photo to your profile that clearly shows your head and no more than your shoulders.