I just browsed through my Whatsapp video folder and checked the details of the longer videos. (in case you wonder where are they: Internal memory of your smartphone->WhatsApp->Media->WhatsApp Video->Private)
I found some with 10-13 MB.
I found these used a horizontal resolution of about 600-640 (which means in OBS you reproduce this with 640x360).
Surprise, surprise, some use a frame rate of only 15 fps! This is a quarter in comparison to 60 fps or half in comparison to 30 fps - quarters/halves file size.
Bitrate is about 500 kb/s, some less.
I don't know if Whatsapp streams the videos or downloads them completely before playing, so you might try to use a constant quality mode like CRF as rate control instead of one of the bitrate-based rate controls such as CBR, ABR. If you have low or no motion in most parts of your video, CRF is destined for producing perfect quality with lowest bitrates. Tune the CRF parameter so you get your desired file size in the end.
It is a very time-intensive process to learn which CRF parameter produces which file size and which visual quality, so you might create some reference "master" video with OBS and too good quality and use a software like Handbrake afterwards to recode to a smaller file size. This way you don't need to always record a new video - you just encode the same video over and over again and vary the parameters. If you use software encoding with Handbrake, you might even squeeze a bit more quality out of the end product, since it is possible to use a preset such as slow or veryslow that OBS isn't able to use, since you have to encode realtime with OBS but not with Handbrake. So it might be a good idea anyway to recode the master in any case.
Lowering the audio bitrate certainly helps as well. Use the smallest values possible (64k). Audio on a smartphone is pathetic anyway, so nobody would hear it.