Can you turn two inductively coupled conductors into a transformer?
In principle you're correct, a (mains) transformer and wireless charging do work based on the same principles.

However there are some differences in the practical implementations that makes combining the two, as you suggest, difficult to impossible.

Mains voltage uses 50 or 60 Hz AC, so quite a low frequency. That means a transformer for a certain amount of power needs to be big an heavy. Notice how some old power adapters are quite big and heavy, these have a 50 / 60 Hz transformer inside.

Modern power adapters like the one you use to charge your phone also has a transformer but one that works at a much higher frequency. In the order of 100 kHz. That means that the transformer can be much smaller and lighter for the same amount of power compared to a 50 / 60 Hz transformer. The difference in size and weight can easily be a factor 10. Also the newer types are much cheaper to make.

Wireless charging usually also works at a frequency of around 100 kHz so indeed you could theoretically combine the two, meaning the high frequency transformer is replaced by two wireless charging transmit coils. But then you still need a circuit to convert 50 / 60 Hz  into 100 kHz.

Such circuits exist, actually that is what is inside nearly all modern mains adapters. However these circuits operate on the rectified AC mains voltage. That's close to 400 V DC and very dangerous especially for those without proper experience.

So while what you propose is theoretically true, it isn't something that you (as a beginner) can design or work with. It is simply too dangerous.

Your best bet is to get buy a ready made wireless charging module which are powered over USB. There are also small wireless charging receiver modules that can be attached to a phone. These are only a couple of $ each and your best bet at getting wireless power transfer to work.