More humid air with higher specific heat capacity: I’d expect the difference to be utterly negligible. Even at 40°C, the isobaric heat capacity of saturated air is only about 5% higher than that of perfectly dry air (~1.05 J/g·K, compared to ~1), and your slightly leaky window is hardly going to be resaturating the entire room.

As for the energy to dry the air, I’m inexpert in this area¹ but under the impression dehumidification is essentially just a byproduct of how compressors work (the evaporator’s low temperature causes water vapour to condense) rather than something that takes deliberate effort—that, if anything, air conditioners are commonly now deliberately revapourising water to avoid dehumidification beyond the desired level.

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¹ But I am trying to learn for part of a project of my own, a velomobile and trailer to be able to live out of indefinitely, where in the ideal case that I haven’t determined is feasible I’d really like it if I could have one compressor to drive food refrigeration, cabin cooling, heating a low-temperature slow-cooker-style oven, and providing my water supply.