The jack [TRS] on your mic is one normally used used for camera mic inputs, rarely for computer mics.
To a computer, that looks like a headphone jack [TRS], not a headset jack [TRRS], which would look like this
To a computer, a simple mic jack [TS] should look like this
Some computers can automatically figure out all the combinations, but few are ever smart enough to be able to tell the difference between headphones & mic if they're both on the same jack type.
A computer will use a simple 'which pins are connected, at what impedances' to try figure this out. Speakers/headphones will have an impedance between 4 - 250Ω, a cheap mic somewhere in the thousands, 2.000Ω or more …but how does it figure it out if there are 'too many pins' for a mic, but 'too much impedance' for headphones? That's where some struggle.
See CableChick - Understanding TRRS and Audio Jacks for a more comprehensive guide.
What you need is a camera mic to headset adapter, such as this one from Røde [who make a lot of mics, for cameras & otherwise].
This will then force your computer to see it as a headset… just without earphones. It may show a phantom output, but you can ignore it.
There used to be additional confusion over the precise pinout of a TRRS jack, but thankfully just about everything has now settled on the CTIA standard.