How strict is KLM with hand luggage dimensions?

My experience is that they are not too critical about it. Unfortunately, because when you see what people drag into the cabin. Anyway, it will also depend on what type of plane and how full it is. I don't think you'll have any problems with it

In February I brought a (phin) guitar in a backpack from Thailand with KLM, the snake/drake head had already been screwed off. I had already planned to pay the extra costs if necessary, because the neck is about 15 cm longer than is officially allowed at KLM. During check-in and boarding, no one said anything about it.
But of course these are not rights…. Theoretically, they can point you to the rules. And may also do so in a bad mood or if "they don't like your head". In addition, they will also certainly check whether your suitcase/bag fits in the luggage compartment/cabin, partly depending on the number of passengers, and will see (extra paid) hand luggage pass by earlier.
You do indeed see a lot that other people have (too) much more hand luggage with them, and it is indeed frustrating. Especially if you can only store your suitcase 10 meters away. But well…. who says they might not have paid extra for that before or during Check-in?

I don't expect any problems with these minimal differences. Apart from the fact that the flight may not even be full yet.

I can't talk about KLM, but I can talk about Lufthansa, where I worked as a steward for 30 years.
I don't think there are big differences between them, because both airlines have to act in accordance with IATA.

In your case, you most likely won't have any problems.

Normally, your hand luggage is only allowed to have a certain size. I know that in the US people are very strict and the promised cages are used there. They exist in Frankfurt too, but as far as I know, they are mainly used when the plane is fully booked or it is a flight to a destination, where we already know that people like to take too much in the cabin.
This is not to annoy people, but to prevent that there is actually too much luggage on the plane, which can lead to accidents in the event of an evacuation.
In addition, you should also bear in mind that the staff you check in are not necessarily from KLM, but can be from an external company, just like in Frankfurt.
I often stood at the door to greet the guests, where we also checked whether too much or too large luggage came on board. Large items were immediately collected and tagged and promoted to the luggage compartment. But then it was almost suitcases and no hand luggage anymore.
As long as the luggage fits under the space of the seat in front of you or at the top of the hand luggage bin, we didn't pay too much attention to the size. At least not 2 cm difference.

It is not strictly monitored
Especially since you only travel with a trolly
Shouldn't that be a problem and you can also bring a handbag
So feel free to travel

I can't say much about hand luggage, but I flew last January with exactly 1 kilo overweight from hold luggage at KLM, had to pay 125,00 euros for exactly that one kilo. When returning to KLM, we asked for an explanation orally and in writing. At Schiphol I was informed that these were the normal rates. Week later asked again in writing for an explanation of how they arrived at that 125,00 for 1 kilo. KLM never responded to my emails. If possible fly with Emirates or Eva. KLM also in terms of service, bad.

Of course you can also buy another suitcase….

I travel every year with a slightly too wide trolley, never had a problem. So no problem.