I have heard of the SGUnited Traineeships Programme which is offered to help the fresh graduates of 2020 and would be trying that out. Besides this, are there any other opportunities around?

I think you have the right mindset and is on track to success already. Indeed employers are looking at what skills do you have and how you can contribute to the team/project. I recommend picking up skills that might not "pay" now but will add value over many years and shld pay off in the future.

Digital skills such as copywriting, video and photo editing, social media publishing and Non-digital skills such as commnunicating effectively, public speaking, and sales. There are boundless paid and free opportunities available online to pick up them i.e Skillsfuture and Youtube.​​​