A hot shower adds water vapour to the bathroom air. The mirror is usually cooler than this warm, humid air. When air next to the glass is cooled to its dew point, some of its water vapour condenses into a layer of tiny liquid droplets. The dew point is not one fixed temperature: it depends on how much water vapour is present. The more humid the air, the warmer a surface can be and still collect condensation.
Saying that warm air can “hold more water” is convenient but incomplete. More precisely, the saturation vapour pressure of water increases with temperature. As the same parcel of moist air cools, its relative humidity rises. Once it reaches saturation, further cooling favours the change from vapour to liquid.
The mirror has not absorbed “steam”. Curved droplet surfaces scatter light in many directions, disrupting the orderly reflection that would otherwise form a clear image. If you wipe a transparent streak while the glass remains below the dew point, new droplets can form over it. Warming the mirror reduces fogging by keeping its surface above the dew point; ventilation reduces the amount of water vapour and lowers the dew point. Fog on a bathroom mirror, dew on grass and droplets on a cold glass all arise from the same condensation process.
https://www.nesdis.noaa.gov/about/k-12-education/atmosphere/what-humidity
https://weather.metoffice.gov.uk/warnings-and-advice/seasonal-advice/travel/how-fog-affects-travel
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