I don't think a "Switch Pro" is happening.
To make a new chip with Tensor cores would be expensive, it's not the like DSi and New 3DS where they basically just kept the same GPU and just overclocked the CPU and threw in some extra RAM. You can't do DLSS 2.0 with just more RAM and higher clocked CPUs ... even the PS5 and XSX can't do DLSS 2.0 in the same way Nvidia does. It requires Tensor cores.
Besides that a Switch Pro "for third party games" in 2021 doesn't make a whole lot of sense as most 3rd parties are moving on to the PS5/XSX, the Switch would need a full next-generation architecture to be able to get any of those ports.
I don't think Nintendo is aiming for those 3rd party games to be released on PS5 and series X because there are truckloads more of AAA third party games available on PS4 and XBoxOne and Nintendo is simply targeting these demanding games to help carry the Switch next year onward. So whatever Nvidia and Nintendo are planning, it's probably a Switch Pro or Switch 1.5 and not a Switch 2.