Each "robot" requires its own Windows desktop. You might have a sever hosting multiple virtual desktops depending on its resources. Depending on the application(s) being automated, the application(s) may require the desktop session to remain unlocked (some applications behave differently when the desktop is locked and do not present their full UI to be automated). If this is the case, you cannot simply have one "machine" logged-in a several different users to complete the tasks. This might work if your application(s) operate as expected when the computer is locked, however it is not reccomended.
If you have tasks that many users are waiting on responses to, perhaps RDA (or a combination of RPA and RDA) would be most appropriate for that use case; especially if they already have the application(s) running on their desktop.
Scaling can be easily accomplished by adding a new machine and setting it up to connect to the console. The console will then provide it work once it comes online.
If I get you right, the answer for the question "What is the best architecture for the requirement to handle 1000 tasks simultaneously?" is to use 1000 virtual machines. Assuming there is no way to use RDA.
I would suggest you ask more questions about your requirement. The requirement to run 1000 tasks simultaneously is not very specific. I would ask the following:
how long does the task take to perform?
how many total tasks are to be accomplished (hours of operation)?
what is the SLA on returning a result?
are the tasks already queued when the robots are started or does work arrive randomly?
which applications are you performing automation on and do those applications allow multiple instances on a single machine?
With a better understanding of these requirements you can design a solution that will meet the requirement. If the SLA is 60 seconds and the task takes 2 seconds then the need for simultaneous robots is less. If work is pre-queued the answer will be a different result than when the work arrives randomly.
RPA as Thomas said is currently limited more by the applications that are being automated than by anything else. The correct answer to a question like yours cannot be determined without a deeper dive into the requirements.