Noise from the transmission

After my lap I noticed that with the bike off and in neutral the transmission is noisy. I noticed the chain a bit tight, I removed the chain and it seemed a bit hard to bend so I will wash it with diesel and dry it and finally grease it, once mounted I will adjust the chain play. But now I have noticed that the pinion is noisy.

https://youtu.be/dyJUIxiZ7So
The shaft has no signs of wear and has no radial clearance that suggests bearing failure.

I disassembled and washed the chain with diesel. Then I cleaned the pinion and crown with a scraper. The chain links were a bit hard to move so I started to rotate the links one by one and the chain has softened, now it looks ok. I reassembled everything and adjusted the chain slack because it seemed a bit tense before. It now appears that the transmission makes a normal noise when I move the bike from off and in neutral. To grease the clean and degreased transmission, I raised the bike on a lift stand, turned on the bike and engaged the first gear and so I greased the chain while it was in motion. I noticed an annoying shaking every 4-5 seconds of the transmission, as if the engine had misfires. I played with the mixture screw but even if I could hear the engine go from a dry tone to a lower and softer one, the problem of misfiring does not go away.