Is my iPhone 12 waterproof if I put it in the pool underwater and take a picture?

No. Do not submerge your iPhone for any reason. Its water resistant to a degree. It can stand rain, or splashing, but it should not be submerged.

See here for details: link-> About splash, water, and dust resistance of iPhone 7 and later - Apple Support

To prevent liquid damage, avoid these:

• Swimming or bathing with your iPhone
• Exposing your iPhone to pressurized water or high velocity water, such as when showering, water skiing, wake boarding, surfing, jet skiing, and so on
• Using your iPhone in a sauna or steam room
• Intentionally submerging your iPhone in water
• Operating your iPhone outside the suggested temperature ranges or in extremely humid conditions
• Dropping your iPhone or subjecting it to other impacts
• Disassembling your iPhone, including removing screws

Warranty is voided if the water sensors inside the iPhone are triggered.

No.

It is water-resistant(not waterproof). But that can also degrade over time.

Don't put it in the pool on purpose! The water resistance is there to maybe save you from having to buy a phone in case of an accident. But it is not made to be an underwater camera!

Water damage is not covered by the warranty

Water and other liquid damage to iPhone or iPod isn't covered by warranty - Apple Support

And yet water damage will void the warranty, and Apple will not fix it, and in fact advises against submerging it.

Do not submerge it unless you want a damaged iPhone. It may not happen the first time or the fifth time, but once it does happen Apple will not replace it under warranty.

You are entirely on your own if you decide to do that.

There are LOTS of ways to take underwater pics starting under $20.

Examples:

https://www.bhphotovideo.com/c/search?InitialSearch=yes&N=0&Ntt=disposable+camera+waterproof&c3api=4680%2C%2Cdisposable+camera+waterproof%2Ce&msclkid=5f798b0626be1abfe319ebf27b4fed64

DON’T use your iPhone.

Yes, did you also read the entire page?