Unfortunately if you plug anything in the headphone jack it will override the speakers, because its a combo jack. You can still use your mic, but you would need to use headphones, using a breakout like this. You can see it separates the headphones and the mic as separate jacks. Personally I did this yesterday for a Zoom call.

I believe To accomplish what you want( using this mic, with your built in computer speakers), you can get an rather inexpensive USB audio interface $8 USD and use the Mic input and change the playback or output device to you built in hardware.

You would use that included TRRS to TRS adapter with the 2 solutions above.

As I was typing I just realized there is one may be one more option that might not cost you anything. If you plug your computer to an External Display via HDMI like a television you can output the sound using those speakers in the TV. While just plugging in the mic to the computer. If you just have a monitor, some may have a headphone jack that outputs the HDMI audio,

Sounds like you are familiar with the Sound Devices settings, just make those settings accordingly.

I do have to point out that you should keep the level down to minimize feedback or echos.