I forgot to add the new audio that I took after topping up the engine oil and starting it again. I have attached it to this post. It's actually a video but it's very dark. I just did it for the sound in the evening. There is a point where I place the camera closer to the engine (which is when the volume increases slightly) so that one can hear more clearly the rattling of the valve train (47 second mark).
So, to answer your question, yes it seems to be running fine apart from a little more top-end noise than when I last had it running properly.
Note: I forgot to put an SD card into my camera when starting up the car for the first time after putting the oil in. So, I don't have a recording of how the noise went down after a few seconds, but it was very noticeable. The rattling was very bad and after 4-5 seconds went right down. I'll check the oil level again and top it up if needed in the morning and do another test.
Video (Click to make bigger)
Sunday, September 25th, 2022 AT 7:18 PM