Home pod mini

I don't have a definitive answer for you, however the following comes from HomePod mini - Technical Specifications - Apple:

Electrical and Environmental Requirements

• Operating temperature: 0° to 35° C (32° to 95° F)
• Relative humidity: 5% to 90% non-condensing
• Operating altitude: tested up to 3,000 metres (10,000 feet)

Given steam from a shower is often heavy enough to condense on surfaces this might caution against using HomePod in the bathroom, in addition to the general widom to avoid having electricity around water.

tt2

Yes it might damage it, which would void the warranty since they advise not to use near water:

Avoid liquids

Don't use HomePod near water or where it might be exposed to dripping or splashing. Keep HomePod away from all sources of liquid, such as drinks, washbasins, bathtubs, shower stalls, swimming pools, spas, and so on.

For more information, see the HomePod User Guide.

Cleaning and taking care of HomePod - Apple Support

It’s also not safe as tt2 mentioned. Outlets in bathrooms are designed to use with razors, some hair tools etc,

We all know how much water is on the mirror after we shower. That’s how much would be going onto the HomePod.