I just chatted with a Microsoft support centre engineer and he solved the problem! His name is Kehinde.
What we did was he created a link for me and I went in a Cognito browser and I was able to see the chat box next to the hand!
Great to know it works now and many thanks for the share!
By the way, since the Microsoft Q&A community has a policy that "The question author cannot accept their own answer. They can only accept answers by others.". and according to the scenario introduced here: Answering your own questions on Microsoft Q&A, I would make a brief summary of this thread:
[Microsoft Teams : Can not see chat box]
Issue Symptom:
"I use Teams for a meeting and when I logged on a meeting, I used to see the chat box on the right side below or above the People the so that we can chat along a meeting. But somehow that chat box stopped appearing on my screen. I am not able to read or write on a chat box/thread to communicate with my colleagues while we are on a meeting. I checked the setting but can not find a chat box there either..."
Current status:
A link was created and you went in a incognito browser, from where you were able to see the chat box next to the hand.
You could click the "Accept Answer" button for this summary to close this thread, and this can make it easier for other community member's to see the useful information when reading this thread. Thanks for your understanding!