Even defining the address space is not trivial, with things like virtual vs. physical ("32-bit" x86 since the Pentium Pro actually has 36-bit physical addresses) and bankswitching (common on MCUs).
Likewise, data width is equally as complex: the Z80, commonly known as 8-bit, actually has operations on 16-bit "register pairs". 32-bit x86 with MMX has 64-bit registers, and with x87 has 80-bit wide quantities manipulable in a single instruction.
It just so happens that we hit a sweet spot for many years with "32-bit" x86 which had 32-bit integers and pointers, but the subtleties of classifying a system as being n-bit remain.
That said, some systems (mostly mainframes/supercomputers) are "true 64/64-bit" with 64-bit registers and 64-bit address space.
"The AMD specification requires that the most significant 16 bits of any virtual address, bits 48 through 63, must be copies of bit 47 (in a manner akin to sign extension). If this requirement is not met, the processor will raise an exception."
https://en.wikipedia.org/wiki/X86-64#Virtual_address_space_d...
Not at all a safe assumption in general; architectures evolve over time, and in addition, that address space is split such that kernel addresses have those bits set, not cleared.
48-bit byte-addressed: 256 terabytes
48-bit word-addressed: 2 petabytes
56-bit byte-addressed: 64 petabytes
56-bit word-addressed: 512 petabytes