16 bit DAC microcontroller
It's possible that what you want is made, but most DACs you will find built into an MCU would not have more than 12-bit resolution.

In fact simple static DACs of 16 bit resolution are not all the commonly built or used, and are unnecessary for audio.  Instead, more complex technique such as Sigma Delta modulation are typically used.

The classic solution of your problem would be an MCU with an I2S interface (or generic synchronous serial implementation able to interoperate with I2S) feeding an external sigma delta audio DAC.  Many the STM32 series (and likely other lines as well) have such an interface, and its typically something you can select for when using a distributor's online catalog matrix tool.  You may also want to consider making sure you can find code examples for a chip which are adaptable to your need, as figuring out how to operate a peripheral (especially one you would probably want to feed via DMA) from scratch can be a bit of a project.

If your needs are not particularly strict, you might also simply be able to use a PWM output from an MCU timer and an analog lowpass filter.

And yes, there are some parts with 12-bit DACs that you might be able to time modulate to squeeze out another bit or two.

Something you will discover is that it is by no means trivial to design the power and surrounding circuitry in a way that is quiet and linear enough for the limitations of a 16-bit representation to become apparent - it can be done, but a first attempt is unlikely to result in that performance.

A request to identify specific chips would be an off-topic "shopping question" not permitted here.