2021 Street Twin Clutch Is Very Jerky At First Start Of The Day

Hi!

I bought a 2021 Street Twin a month ago and ride it everyday since.
The bike has 33000km on the clock.

I noticed a very weird and uncomfortable issue with clutch during the "first ride of the day", in the morning, when the bike is totally cold (and the weather is too, it's never exceeding 2°C outside when I start the bike).

The problem is that the clutch is very jerky the very first time it engages. At the next traffic light stop, it's almost totally gone and working normally.
I put some throttle (or not), and it changes nothing. It really is like if the clutch disc suddenly engages then disengage then engages again, and again.
No special jerky feeling in the clutch lever.

The very first and initial engagement of the clutch is impossible to get smooth, throttle or not, no mater how gentle and very slooooow I am when releasing the lever.
It’s even worst with throttle because the engine is going faster so when it engages the jerk is bigger.
It makes me look like a gui that never rode bikes and do not expect the bike to move, like my hole body is jerking because of this.

before riding I let the bike get a bit warm, like 2 minutes engine on, time to put gloves and helmet on.

Engine oil is 10W40 so it should be totally fine.
Full service history in triumph official dealer, the bike has always been well looked after.

Another thing and I don't know how it could be related but I mention it here, it's pretty hard to find neutral on my bike, not something I read a lot with the 900cc engine/gear box from T100 ans Street Twin.

I'm rinding for 15 years now and never had this feeling in any bike.

I'm used to do maintenance by myself and clutches is something I've done few times, if needed.

Thanks for your thoughts and help!

Also here is a picture of my beautiful bike ^^.

Guillaume