I struggled to find a solution for this for days so I wanted to share my situation. I'm converting an existing ASP.NET MVC application over to ASP.NET Core MVC. However the biggest change with using the ASP.NET Core, is that the System.Web namespace is a no go. However typically, SQL Server Reporting Services (SSRS) is typically added as a WebReference to a project, which is based on - you guessed it, System.Web.
So I needed to find an alternative way to be able to hit the SSRS endpoint for executing reports. For my scenario, I primarily wanted PDF's (though the call to SSRS's Render method allows you to pick what the export format is).
The solution to this problem presented it's own problems, most notably an error to the tune of:
Microsoft.ReportingServices.Diagnostics.Utilities.MissingSessionIdException: The session identifier is missing. A session identifier is required for this operation.
So my two questions I ended up answering that might be of value to others were, How do I use SSRS without System.Web, and how do I solve the error about "Missing session identifier"