> [Thumb] cuts down the instructions as well as the data to 16-bit symbols
Wrong. The original Thumb instruction set has 16-bit instructions with reduced functionality, most notably many instructions can access only the low 8 registers. The register size is still 32 bits. Thumb2 extends the instruction set with additional 32-bit instructions providing full access to the entire architecture.
The 64-bit ARM has no equivalent of Thumb mode, although 32-bit ARMv7 userspace is still supported.