I will provide a full answer based on answers given here and elsewhere.
So my recording was a total mess: sounds crackling, popping, with the sound of the processor, or the fan of the laptop.
What I did was to input the following commands:
1/ Restore alsactl
It improved tremendously the quality but was still bad.
2/ Adjust microphone with Alsa mixer (Rajashekhar Ch's answer)
Fn + F4
Bring capture to !30 and microboost to ~50
3/ Followed Mohammad's answer:
edit /etc/pulse/default.pa by adding at the end:
### Enable Echo/Noise-Cancelation
load-module module-echo-cancel aec_method=webrtc aec_args="analog_gain_control=0 digital_gain_control=1" source_name=echoCancel_source sink_name=echoCancel_sink
4/ Activate Noise cancellation in OBS:
You have to click on the settings button and then filters as seen on screenshot.
Play with the different ranges to see what works best for you.