Is the A1407 cinema display compatible with the 2023 16" Macbook Pro?

A1407 is the 27" Apple Thunderbolt Display, for which you would use the aforementioned adapter.

The 27" LED Cinema Display is model A1316, It requires Mini DisplayPort input, so if you had it, you would not want to use the Apple TB3-to-2 adapter (an adapter that converts only Thunderbolt protocol).

Apple ThunderBolt-3 <-> Thunderbolt-2 adapter, US$50. no additional cables required and your Thunderbolt-2 peripherals on the display keep working, if they have their own power supply (or maybe the display will provide power.)

we were just talking about that over here:

Thunderbolt 4 to Thunderbolt 1 - Apple Community

.

No problem.