From webpage I read: " Search or browse games, applications, demos, graphics, music and tools from the golden age of 32-bit home computing."

But Amiga has a 16 bit CPU... or not?

"From a developer's point of view, the 68000 provides a full suite of 32-bit operations but has a 16-bit external data bus and is implemented using a 16-bit arithmetic logic unit, so 32-bit computations are transparently handled as multiple 16-bit values at a performance cost. Also, while addresses are 32-bit, the chip is limited to 16 MB of physical memory using the lower 24 of the address bits.[35][36] The later Amiga 2500, Amiga 3000, Amiga 4000 and Amiga 1200 models use fully 32-bit, 68000-compatible processors from Motorola with improved performance and larger addressing capability."

https://en.wikipedia.org/wiki/Amiga

It's a bit complicated and it depends on what exactly you're measuring. The 68000 CPU has 32-bit registers internally, the address bus is 24-bit, and the data bus is 16.

I think most Amiga’s had 32-bit registers, but a 16-bit bus.

(So to everything around the CPU they were 16-bit even though internally they could do 32-bit computations)

To me the entire 68K family were always 32-bit CPUs because of the 32-bit data registers. You work with it and write assembly for it in a transparent "32-bit way" like any other 32-bit CPU, with no additional care or work necessary for the programmer in regards to the 68000's external data bus being only 16 bits wide and behind the scenes doing 32-bit transfers in two steps.

Also worth nothing that it's just the early 68Ks that came with a narrow external data bus. The 68020 and onward, which were also used in the Amigas, have a 32 bits wide data bus.