First I'd like to point out that Feynman is not your best resource on the subject of thermodynamics. Other posts have shown that some of his statements, while not necessarily incorrect, can be misleading. It's not his forte.
Carnot assumed that heat cannot be taken in at a certain temperature
and converted into work with no other change in the system or the
surroundings.
I don't think Carnot put it that way. Heat can be taken in at a certain temperature and converted to work. It's called a reversible isothermal expansion process. The changes that occur is there will be an increase in the entropy of the system due to the heat addition, and an equal decrease in the entropy of the surroundings due the same amount of heat being extracted from the surroundings at the same temperature. I think what Feynman meant to say is you can't convert heat into work while exchanging heat with a single temperature reservoir when operating in a cycle. If that is the case, then the statement would be consistent with the next statement, as I have clarified it.
Carnot assumed that it is impossible to extract the energy of heat at
a single temperature.
Missing here is the reference to a complete cycle. The Kelvin Plank statement of the second law says
No heat engine can operate in a cycle while transferring heat with a single heat reservoir
A key phrase is "operate in a cycle". As I said, it is possible to extract heat from a single temperature and do work in a process (e.g., reversible isothermal expansion process), but it is not possible to convert heat entirely into work when operating in a cycle.
Aren't these statement at odds with the concept of heat baths wherein
an amount of heat đť‘„ can be extracted without changing the reservoir's
temperature?
First, with the corrections/clarifications I discussed above, the statements are consistent with each other. What's more Carnot's actual theorem and the Kelvin Plank statement both refer to heat engines operating between two fixed temperatures. The implication is the temperatures of the source and sink are constant during the heat transfer processes.
And so is it the heat baths in the Carnot engine that make the engine impractical?
It is not the heat baths that make the Carnot engine impractical. In practice thermodynamic cycles can operate between fixed temperatures. All that's required is the heat capacities be large enough relative to the amount of heat transfer so that the temperatures remain relatively constant.
What makes the Carnot engine, or for that matter any reversible engine, impractical is that the processes need to be carried out reversibly, or quasi-statically. The requires the temperature and pressure differentials between the operating fluid and the surroundings to be infinitesimally small. That, in turn, means the processes will occur infinitely slowly. So while the Carnot engine may be the most efficient in producing work, as a practical matter the rate at which work is produced (power) would be very low.
Someone said if you put a Carnot engine in your car you would get fantastic mileage, but pedestrians would be passing you by!.
Hope this helps.
