iPhone 13 fell in the tub

There is always a possibility that liquid has entered your iPhone, and to prevent any potential further damage, I suggest that you power-off your phone, and then, take it to your local Apple Store or Apple Authorized Service Provider to have them take a look and provide you with your options.

Should the phone need replacement AND you still have an active AppleCare+ plan, you may find that the cost will be reduced as one of the two accidental incidents that are covered under the plan. If you didn't elect to get an AppleCare+ plan, then any costs would be considered out-of-warranty and you would have to cover them at full cost.

Water and other liquid damage to iPhone or iPod isn't covered by warranty and any other problems the phone may have in the future can be denied repair due to the liquid damage.

Good luck! 🦆

For the future, get yourself a cheap Bluetooth speaker (there are even some designed to be used outdoors or in damp environments) and use that in the bathroom. That way, you can leave your phone safely out of range of the tub.