The chapter on Wi-Fi says this:
10.1 WLAN CPU and Memory Subsystem
The CYW43439 includes an integrated ARM Cortex-M3 processor with internal RAM and ROM. [...] On-chip memory for the CPU includes 512 KB SRAM and 640 KB ROM
And for Bluetooth it has this:
8. Microprocessor and Memory Unit for Bluetooth
The Bluetooth microprocessor core is based on the ARM Cortex-M3 32-bit RISC processor with embedded ICE-RT debug and JTAG interface units. It runs software from the link control (LC) layer up to the host controller interface (HCI). The ARM core is paired with a memory unit that contains 576 KB of ROM for program storage and boot ROM, and 160 KB of RAM for data scratch-pad and patch RAM code.
Strange and confusing.
Edit: quote markup, added mising section number for BT.
[1]: https://www.infineon.com/dgdl/Infineon-CYW43439-Single-Chip-...
Does shows it does have an M4 as you stated, that is for the BT stack.
Imho, non-wireless-intergrated MCUs will go extinct in IoT very soon.
They also have the best mixed signal out of every other scrawny IoT startup who uses off-the-shelf IP.