Well, this worked for me:
Download XCode from https://developer.apple.com/download/all/
Transfer the .xip file to your external SSD.
Extract/Unzip the Xcode from .xip file there.
After extracting, transfer the XCode into your Applications Folder.
P.S I successfully installed XCode 13.1 using the above process on my MBA.
P.P.S I had around 37 GB left on my mac (before installing) and used a 2 TB SSD
DM_17
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