Is it possible to grub the main code from STM32 with built-in Oximeter
For sure the manufacturer has enabled readout-protection, so you're not getting their binary code by simply attaching an ST-Link to it. You could erase the chip but then you'd have a blank chip and that's not much good without a lot of knowledge, a schematic and so on. 

There might be something useful on the serial port, with the aid of suitable tools you could see what, if anything, is coming out of it. Something like a USB-TTL module on RxD and TxD. It's possible it only spits out data in response to a query, in which case you might have more trouble getting anything out of it. With luck there's a boot message in something like 9600-n-1 (or maybe a higher baud rate) that at least lets you read some hello world thing and get the baud rate correct, then you could try sending it a  or whatever and see if it responds. 

The other clock and data, I'm guessing is SPI data to the display, but I could be wrong about that.