Hello folks from Germany and nice to see you all here in Night City!

So, I started as many as you my journey into NC with my nomad character to built her around classic rogue combat style in melee.
But after my first 12 hours, there're lot of open question marks buzzing around my head.
First, melee combat style in hard difficulty mode is pain in the ass and very _hard_ to play. Got my first Tanto knife, put my attribute points in Coolness and Reflex to get stealth and bonuses von crit in melee combat.

Let us get into to Coolness tree. If you look at the tooltip here, it says that every point in Coolness also improves (other things) the damage in stealth mode by 10%.

I understand the stealth mechanics (crouching, dark edged corners on the screen), but that would mean, that this +x% bonus damage in stealth is only considered when opening / entering combat once?

Example: I am stealthing around, getting back of an enemy. Then, my first hit with the melee weapon would deal that +x% damage from the Coolness tree. After that, the enemy recognises me and I'm out of stealth.
Other thing is: Why would a player stand back at the enemy and press the attack with melee button when I can just hit the F button to execute a silent takedown?

Am I getting something wrong here? I would be very interested what your thoughts / first impressions are regarding melee built / combat in CP2077 :)

Yep Enemies have a chance to break the grab (or negate it all together) based off your body stat, which if you're going stealth probably isn't a priority to increase.
Also worth noting - a stealth kill doesn't necessarily require you to approach the enemy from behind, and you only break stealth if someone (like the victim) lives long enough to see it. Not entirely :P For the build it sounds like you're going for though you probably want to invest in a monowire as soon as practically possible, it's basically tailor made for the high stealth / crit build.
Also don't neglect the other areas just because you're going stealth melee. There's some useful quick hacks you might want to invest in (reboot optics and memory wipe) which can be hugely helpful for a stealth run. If you have the money spare, upgrading the cyber deck and a few points into intelligence to be able to take over camera's or set them to friendly (auto-tags enemies for you) is also a worthwhile investment.