The model number BM-800 is used by a lot of different microphone brands for a microphone of the same design (but the build quality can be variable). They are good, low-cost studio condenser microphones
A condenser microphone usually requires phantom power, which is typically 48 volts but many microphones can work with only 9 volts
it will work with my phone
this is not typical for a phantom powered microphone as the phone would only supply less than 5volts of power.
Your laptop might not be powering the microphone through the headset jack at all or maybe even a bit less than the phone, but it will not work well if it can only get a low voltage
I found this article that says some versions have a built in battery charged from a USB port
If your microphone does not have a USB charging socket, you need to get a phantom power supply,
or a microphone preamplifier; mixer or audio interface with phantom power