This is just how browser’s handle relative paths.
You have a Handlebars template that contains the following:
<img src="{{file}}" class="responsive-img">
The value of file is set to uploads/${req.file.filename}, which becomes something like uploads/myImage-1589223958713.PNG.
When your template is executed with above value for file you get:
<img src="uploads/myImage-1589223958713.PNG" class="responsive-img">
When the browser sees a relative URL, like uploads/myImage-1589223958713.PNG, it has to figure out the absolute URL. Since this relative URL does not begin with a /, the browser thinks it is a child path of the current page URL.
If the current page URL is http://localhost:3000/uploaded/uploader, the browser thinks your uploads/myImage-1589223958713.PNG URL is a child of http://localhost:3000/uploader/ and so produces: http://localhost:3000/uploader/uploads/myImage-1589223958713.PNG.
To get the correct URL, you want to set the value for file so that it includes the full path:
file: `/uploads/${req.file.filename}`
Update:
Note that /public should not be included in the value for file because the /public directory is registered with express as a directory in which to look for static assets.