Question: My supervisor started the e-mail thread of welcoming me to the team/department. Several team members has already replied (including the boss of my supervisor so I'm extra nervous) with a brief but warm welcome message. I was wondering what is the best way to reply in this thread.

This is my first fully remote role so I am not that familiar with how it works yet.

Would a short reply like "Thanks for the warm welcome, I'm excited to be working with everyone and I'm looking forward meeting you in the upcoming weeks." or Should I be adding my professional background/main tasks of my role/hobbies/etc. ?

Answer: 
I will disagree with other answers: apply the desk decoration test. If the culture of the company is such that you would keep some decoration on your desk that related to your personal life (picture of your pet, funny mug about your hobby, whatever) then you can include something relating to your personal life in your intro e-mail (*if you want to*).

It basically serves the same purpose as having something on your desk: it marks a topic as being safe to ask about. Since a lot of people have things they don't want to talk about\*, having a clear indication of a good topic is a kindness to your teammates, and will make it a lot easier for them to start talking to you. You don't need to go into any detail, just enough so that the topic has been opened and people can talk to you personally if they want to. (\*And some people don't want to talk about *anything*.)

The main difference between remote and in person is being more deliberate about sharing information, since a lot of cues (e.g. the funny desk mug) are missing. (As well as deliberate communication about work-related things, instead of "just have an open office plan and everyone will collaborate automatically"...ha, ha.)
It's human nature believe it or not for people to want to help, show or instruct others so use this to your advantage because you won't be able to later on. Very graciously thank everyone for the welcome and then fall on your sword and concede very briefly and in the tamest way express your appreciation for those who will bare with you and understand that there are things you will have to learn and appreciate their understanding and help........ I am truly taken back at how welcomed I have been made to feel. I look forward to working with and getting to know you all. I'm hoping to get up to speed as quickly as possible and appreciate in advance your patience and understanding in learning the ways of this new endeavor. I am so excited and grateful to be here. Thank you all again.