The answer is yes, you can get a 2nd SDIO port out of a raspberry pi 4.  The trick is to solder the right GPIO pins to a cheap USB card reader.  Remove the brain from the USB card reader with hot air.

The 6 SDIO signals except for GND & 3V are given.

Then add the following to /boot/config.txt:

dtoverlay=sdio,poll_once=off

The trick is it's only documented for 32 bit raspian.  Presumably 64 bit ubunt would require rebuilding a kernel with a custom device tree.  Maybe it's a practical way to have more storage without getting a bigger SD card or a way to access a full sized SD card.  The mane use is adding wifi to a raspberry pi zero W with a broken CYW4343W, a common situation.

SDIO wifi modules are obsolete & very expensive.  There is a way to hack an ESP-12F into an SDIO card.

https://hackaday.io/project/8678/instructions

https://www.adafruit.com/product/2491

The ESP-12F specifically is just an ESP8266 with flash.  The instructions don't show any specific connections, but it's believed desoldering the flash chip exposes a bunch of SDIO pins.  The datasheet for the ESP8266 is required to know the pinout.

The lion kingdom has a bag of ESP8266's which could restore wifi to the broken raspberry pi zero W.  They've just never had a use.