I went ahead and used the command to check what the Wireless Card was of the RPi4, and I got the code to be VL805 by VIA Technologies, Inc. Is this wireless card compatible with airmon-ng? If not, what should I do to get airmon-ng to work? I am trying to change my wireless card to a monitor mode.
If you want to sniff your neighbors WiFi, the wireless chip must support monitor mode. The built-in WiFi on a Raspberry Pi does not support it. So you are without luck. You can check it with:
rpi ~$ iw list
and look for
Supported interface modes: in the longish output. Have a look at Enable monitor mode for further information about this.
The dmesg log shows that the driver is loaded for a BCM4345/6 chip. It may be worth you checking this on your board as the RPT/RPF have not stated what this chip is as far as I know (and it's not in the certification documentation).
This note from Kali Linux here states that you can get:
on-board wifi monitor mode & frame injection support
airmon-ng will report what it thinks the chip is and running
airmon-ng check will tell any software clashes.