Currently, there is no possibility to view the LWC code from your salesforce browser (developer console).
In this post, you will look around a way of viewing and editing a lightning web component in salesforce org.
You can approach this requirement using a chrome extension available as Salesforce advance Code searcher.
It provides the flexibility to view and edit a lightning web component(html,css,js) file available in salesforce org.
First of all, you have to add the above extension to your chrome browser and I guess you had already performed this activity. After adding, you can go to set up home, and then you are asked to authorize your org. Once you are authorized you will land here pasted below.
Hurray!!this useful chrome extension help in achieving our requirement.
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