There are two ways to view the source of a Chrome extension:
Method 1) Without Installing the Extension:
You need to download the extension. For that go to the extension download page and note down the extension ID, which is the last part of the URL (after the last slash). It would be something like: bmihblnpomgpjkfddepdpdafhhepdbek
You can download the extension at this URL (replacing <EXTENSION_ID> with actual ID):
https://clients2.google.com/service/update2/crx?response=redirect&os=win&arch=x64&os_arch=x86_64&nacl_arch=x86-64&prod=chromiumcrx&prodchannel=beta&prodversion=79.0.3945.53&lang=ru&acceptformat=crx3&x=id%3D<EXTENSION_ID>%26installsource%3Dondemand%26uc
For the above ID (bmihblnpomgpjkfddepdpdafhhepdbek), it would be :
https://clients2.google.com/service/update2/crx?response=redirect&os=win&arch=x64&os_arch=x86_64&nacl_arch=x86-64&prod=chromiumcrx&prodchannel=beta&prodversion=79.0.3945.53&lang=ru&acceptformat=crx3&x=id%3Dbmihblnpomgpjkfddepdpdafhhepdbek%26installsource%3Dondemand%26uc
This will download relevant .crx file.
Once the .crx file is downloaded, you can easily get the code by extracting files packed inside it with 7-Zip
Method 2) After installation of extension:
It is much easier after installation. The extension is installed at:
Windows: C:\Users\<user_name>\AppData\Local\Google\Chrome\User Data\Default\Extensions\
Linux : ~/.config/google-chrome/Default/Extensions/
There are folders with IDs, e.g. bmihblnpomgpjkfddepdpdafhhepdbek. Inside the ID folder you will find the source code.