Per my experience, I don't think this is an IIS issue.
It seems that you are serving static files by your own way.
In the Azure Web Apps, we don't need to do that,
if you take a look at the following lines in the web.config
file you will find that the IIS server already handles serving up the static content such as images, CSS files, and JavaScript files from the /public directory.
So we can just add a folder named public
under the project's root directory and then put the static files in where.
<!-- First we consider whether the incoming URL matches a physical file in the /public folder -->
<rule name="StaticContent">
<action type="Rewrite" url="public{REQUEST_URI}"/>
</rule>
For example, the project structure looks like this,

If you are using Express, you can also do the same thing with the code below,
app.use(express.static('public'))