After encountering extreme under extrusion on my Anycubic i3 Mega, I first cleaned the nozzle and ended up replacing the entire hotend + nozzle. Since that did not help and I couldn't see any issues with it, I went on to check my E-steps. It seems that this is the root cause of the issue.
I removed the Bowden tube to have no resistance and used
G1 E100 F100 to feed 100 mm of filament through the extruder. The extruder only extruded ca. 23 mm though, so I had to adjust the E-Steps value from 92 to 398 which already seemed way off, seemingly "fixed" the issue though. When I repeated the test "under load" with the Bowden tube connected and the hotend heated to 220 °C (using PLA I normally print at 200 °C), the extruder once again only extruded a fraction of the supposed 100 mm (I don't remember the exact measurement, though approximately 30 mm). The gears seem to be fine, and the filament that is pushed against the small gear doesn't seem to slip either.
Unfortunately, that's where my experience ends, can someone tell me how to proceed to narrow down the issue? I suppose it could be the motor itself, a faulty stepper motor driver, loose cables, or the mainboard.
Edit to @Citadel: When I bought the printer it had a spare hot end that came with it. I simply replaced the old one with this one. I did not do any further hardware customization.
Edit2: Sorry for the late update, I wasn't able to check the printer before due to work. I swapped the stepper driver with one of the others on board and checked the e-steps again. Aaaand I just then I noticed I must have forgotten to save the to eeprom when I updated the e-steps last time... So of course I tried with the swapped stepper driver and original e-steps (92), but this didn't fix the issue. So the issue is not the driver. After that I changed the e-steps to 398 again and saved this time. Last time I accidentally started a print that that caused the eeprom reset before I saved the settings and tried the e-steps under load. This time it worked, even under load. I still believe this must mean that the motor is missing some steps but for now it seems to print fine. If I get issues again I'll next try to swap the motor. Thanks for your answers!
TL;DR: forgot to save the new e-steps due to starting a calibration print that reset the value before saving. New value actually works but probably indicates that something might be wrong with the motor as the stepper driver is fine.