Hello @Riyaz Patanwala and welcome to Microsoft Q&A.
Unfortunately, the web activity feature you are pointing out does not do what you think it does. To my understanding, it takes the definition of the Linked Service / Dataset and adds it to the body. It does not let you put the actual data into the body. A very niche case in my opinion.
Instead, the method I use to pass data in web activity, is to first fetch the data using another web activity.
That is, first a web activity points to the blob you want to read. This fetches the data and makes it available in the activity output.
Then re-use the output in the body of the "Insert Data" web activity.
Below are details of how to set up the reading web activity for blob.
URL: https://myStorageAccount.blob.core.windows.net/myContainer/myFolder/myFile.txt
Headers: x-ms-version 2017-11-09
Advanced -> Authentication: Managed Identity
Advanced -> Authentication -> Resource: https://storage.azure.com/
By selecting Managed Identity authentication, you need to go to the storage account, and grant blob reader / blob contributor role to the Data Factory.
In the body of "Insert Data" use something like @activity('Get stuff').output.Response to pull in the results of the read.
Do keep in mind, the Web activity returns at most 4 MB of data. If your file is bigger, you may run into problems.