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.
In general I don't think a Switch Pro that is decently beefed up is going to happen a la Pro/X, but its more likely than "Switch 2 in 2022" some people on here are saying. Was just doing some wild speculation as people seemed to think this meant new hardware coming soonish when obviously Switch 2 is a long way off. Most likely this chip is for early R&D for a chip that'll be out in 2 years and in the Switch 2 in 3.5 to 4 years.
There will no doubt be a Switch Pro, but yeah whenever I say Pro or Plus or Premium or whatever related to Switch I don't mean a mid-gen hardware upgrade like Pro/X, I mean like what Nintendo always does which is make a better updated version to keep the highest price point high and get some early adopters to doulbe dip on the system. Larger screen, more storage, hopefully bluetooth, maybe a little bit more power to run games a tiny bit smoother or high res - to me those would be the main things a Premium Switch would get at.