I get an Access Violation because WebModule2=nil. To try to address this I moved the definitions to the TWebModule2 unit, but it didn't help - the library unit consists of (essentially)
begin
  CoInitFlags := COINIT_MULTITHREADED;
  Application.Initialize;
  Application.CreateForm(TWebModule2, WebModule2);
  Application.Run;
end.

The TWebModule2 unit now looks like this:

unit webint;
interface
uses ...

type
    TAS_IBODatabase = class(TIBODatabase)
    private
    public
        constructor Create(anOwner: TComponent); override;
    end;

    TAS_IBOQuery = class(TIBOQuery)
    private
    public
        procedure Open;
        constructor Create(anOwner: TComponent); override;
    end;

  TWebModule2 = class(TWebModule)
     AS_DLL_SESSION: TIB_Session;
     AS_DLL_TRANSACTION: TIBOTransaction;
     procedure WebModule2USERLISTAction(Sender: TObject; Request: TWebRequest; Response: TWebResponse; var Handled: Boolean);
    ...
   end;

var
  WebModule2: TWebModule2;

implementation

uses ...

constructor TAS_IBODatabase.Create(anOwner: TComponent);
begin
    inherited Create(anOwner);
    if Assigned(WebModule2) then
        WriteErMsg('WebModule2 IS assigned')
    else
        WriteErMsg('WebModule2 IS NOT assigned');

    IB_Session := WebModule2.AS_DLL_Session;  {Generates AV}
    WriteErMsg('Successfully executed "IB_Session:= WebModule2.AS_DLL_Session"');
end;

procedure TWebModule2.WebModule2USERLISTAction(Sender: TObject;
  Request: TWebRequest; Response: TWebResponse; var Handled: Boolean);
...