Calories and heart rate?!

Yes, it should, but it depends on the exact model you own. Diverse Garmin models employ diverse Firstbeat algorithms. Newer models use more sophisticated methods than the old ones. Read more about the methods for example on the following pages - they explain it in finer details

• https://www.firstbeatanalytics.com/en/features/calories-burned/
• https://www.firstbeat.com/en/blog/firstbeat-gets-calorie-counts-right/ 

Fenix 6 pro...

It's the newest model, hence it supports the advanced methods.

link refers to moments of sport, when the VO2 detection is activated ... but in everyday life? and also able to recognize during the day if the increase is caused by anxiety and stress or by actual 'intensity'?

Yes, it is. It has nothing to do with VO₂Max. It is detected witth he help of HR Variability, which is monitored permanently (you can see it also on the daily Stress graphs)

but last week as soon as I woke up and after having made about 200 steps, the beauty of 50 calories ... and only because my heart rate was very high (I had not slept and woke up with a start) no physical effort .. .only 200 steps around the house, in theory it shouldn't confuse anxiety with actual activity

50 Calories in what time? Including the RMR or just active ones? Including the sleep, or only afterwards? You can burn Calories over RMR even while sleeping, especially after workouts.

50 active calories in just under 30 minutes ... since I woke up to leave the house, took about 200 steps ... I had a high heart rate (90-100 beats ...) and for this reason that then I asked the question about whether the garmin distinguished between a high frequency given by anxiety or by sport

Always sorry for my english ...

Your English is fine. The majority of users here are not native English speakers anyway (myself including), and those who are, are often not guaranteed to write in Oxford English at all 

4014744 said:

and for this reason that then I asked the question about whether the garmin distinguished between a high frequency given by anxiety or by sport

Yes, I answered that already. It should. You best post the screesnhots of the HR graph and the Stress data for the concerned time, so that we can judge better, why you burned 50 Calories in 30 minutes. It is not impossible - some trivial daily tasks can burn quite a bit. For example this website claims that the average person will burn 250-300 calories per hour cooking and doing food preparation (seems a bit high to me, I guess it is including the RMR), so if you prepared your breakfast, dressed, washed, etc. it would not be surprising if you burned 50 kcal in 30 minutes.