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GDP is measures dollars in the numerator. This is the same concept of retail sails increasing in terms of dollars sold, but decreasing in terms of actual things sold.

Does a dollar denominated analysis like that inherently bake in inflation (real, not nominal)?

I don't think this correct. Many industries in north America are still not producing at precovid levels.

For example:

https://fred.stlouisfed.org/series/DAUPSA

That graph shoes a long-term decline. The pandemic has just accelerated things toward their natural conclusion.

Up over 2020 which saw a global pandemic and a shutdown of most of the developed world.

Did you look at the graph? 2021 is higher than 2020 and 2019. Presumably because manufacturing was trying to catch up with a backlog.