Does the Commodore CDTV-CR contain a 65C02 for some reason?
Yes, but it's a rather plain (NMOS) 6500 core.
Or, if it's emulating actual hardware, where is the 65C02?
Hiden in a CSG 6500/1 microcontrollers (*1)
All Amigas used variations thereof. They are basically a 6503 CPU (*2) plus a 6531 RRIOC(*3) with RAM halved to 64 Byte (*4) joint in a single chip. Base type number is (usually) 6570/71.
The Amiga 500 contained the same 6500/1 as the Amiga 3000, here called 6570-36 (part number 328191-02), while the Amiga 1000 had a 6570-33 (*5).
For the CDTV a version named "Remote Control Input Converter" was made to handle things like joystick input. It got no chip type stamped on, but a part number (252609-02).
The CD-1221 Keyboard itself did contain another 6500/1, this time stamped as 6571R6PD, part number 315107-01, doing the matrix scan much like with any other Amiga keyboard.
So you see, there may be even more than just one 6500 with a CDTV.
See this fine page for more details of 6500/1 usage within Commodore products as well as pinout and usage for the CDTV.
*1 - As the name hints, they are not really a MOS/CSG design at all, but Rockwell's first 6500 microcontroller.
*2 - Internal address bus is just 12 bit (PC is still 16).
*3 - The 6531 RRIOC (ROM-RAM-I/O-COUNTER) is a less known type of the 653x family. Mostly like a 6530, but as well available in a quite unusual 52 pin DIP offering additional Ports C (8 bit output) and D (4 bit input only), as well as battery backup for the RAM. It offered 128 Byte RAM and 2 KiB ROM
*4 - Or a 6503 CPU plus a 6532 RIOT with RAM halved to 64 Bytes plus a 6540 ROM and modified ports. Or a 6503 CPU plus 6530 RRIOT with ROM doubled to 2 KiB and Pick your choice. In any case it's a selection of chip components used before arranged to form the 6570.
*5 - The postfix seams to denote a ROM version/revision, much like it was always done by MOS/CSG when it came devices containing ROM, like with the 6530 RRIOT or 6540 ROM.