From the Video you have shared, the engine sound quit harsh and also tick-tick is there.
I have to admit it sounds like my engine

(70,000km), and I don't know of any other CBR250R engine sound for comparison. So I wrote "OK".
It's just that
Tony seems to have a hard starting too, then he turns the throttle to help the engine run in the first few seconds???
Because my hard starting problem(
LINK) is still not solved and I thought it was,
I have new claims, and it has to do with engine noises:
In my opinion, because this is the last thing I haven't tried yet, I have a slight compression leak, and after a few movements of the piston and a few detonation cycles, the heat causes the rings to expand and the clearance to close (because after a few seconds my engine settles).
I did a compression test
LINK, but it turned out that it has no contribution to understanding the situation because it is very inaccurate.
So my rings seal good after a seconds and I get good performance, but if this is the case, then there is also clearance between the piston and the cylinder, and probably this causes a ticking type of noise. I don't have an oil leak, burning the fuel is normal. But....
I share it because It seems to me that this is part of the noise "problem" at used engine (70,000Km).
I can do a top engine overhaul...but I have no reason to rush, maybe next winter? Right now summer is coming, and when the temperatures continue to rise, in my estimation above 25 degrees, the first morning start will return to normal (without the need to lightly pull the throttle).