How are CPU architecture and word size related?

I did lot of research on internet but couldn't get my answer. I want to know what is the difference between the word size and CPU architecture?

For eg.- I read that CPU of 32-bit architecture can address 2^32 memory locations. Now if we consider that one address points to a single byte, then it means we can have memory size of 2^32 Bytes. We can call it byte addressable memory. Now, I also read that word size is the size of register in a CPU, i.e., it is the minimum no. of bits on which a CPU works upon.

So, help me understand here what is the word size of this computer organization? Is it 32-bit or 1 Byte (as memory is byte addressable)?

What if one address could point 2 Bytes of data instead of 1 Byte? What would be word size then?

Consider the following link.

GATE CS Questions on computer organisation

Question no. 3 from this link is as follows-

A machine has a 32-bit architecture, with 1-word long instructions. It has 64 registers, each of which is 32 bits long. It needs to support 45 instructions, which have an immediate operand in addition to two register operands. Assuming that the immediate operand is an unsigned integer, the maximum value of the immediate operand is

Now, the very first line of the solution says-

As machine has 32-bit architecture, therefore, 1 word = 32 bits = instruction size

How can we say that since CPU is 32-bit, word size is also 32 bit. Doesn't 32-bit architecture just mean that the no. of addresses in the physical memory is 2^32? And also doesn't the word size mean the size of memory each of those 2^32 addresses would point to?