You're using QSV encoding, which utilizes GPU rendering resources. Your GPU is badly overloaded (causing the rendering stalls), and then overloaded again by the encoding (the encoding lag).
I'd recommend switching to x264 Ultrafast encoding, and running OBS as Admin. This will move the encoding load to your CPU (unfortunately a U-model, which are ultra-low-power aimed at battery life) and allow OBS to take GPU priority to complete its housekeeping tasks before the game can eat the rest.
It's because your system is indeed very weak. Minecraft is extremely lightweight, and Phasmophobia is still in early-access (so not super well optimized).
On the up side, since you're just local-recording, you can use x264 Ultrafast to keep the CPU load as low as possible, and if you record using CQP/CRF (instead of CBR, which you NEVER should use for recording anyway) it will automatically use more bitrate to compensate for the poor encoding quality.