What is the name of the device that combines and synchronizes two AC sources into one?
There are two tasks similar to your request.

Connect an AC-generator to an AC-grid.
Uninterruptible power supply.

To connect the AC-generator to the AC-grid (and prevent the AC-generator from becoming a load) you must:

Set the amplitude from generator equal to amplitude from the grid
Set the same frequency
Set the same phase

These functions are commonly integrated in the generator controller.
To make uninterruptible power supply an AC-DC-AC chain is built. This chain as well as frequency and phase tracking is also included in the UPS controller.
P.S. There are some similar systems like HVDC Cross-Channel but there cost is much more than 450$
If we are talking about rampage of green energetics with local solar panels, wind generators, litium batterys and connection to the common AC-grid then you may look at something like Kinergier Pro (350$).