If the rules where different the world would be different but My character in game knows I survived being hit x times by a giant...
No, he doesnt.
When he survives an encounter with the giant, losing half his HP in the process, he probably hasnt even been physcially struck once. He cant tell the difference between the Giant missing his AC or hitting his AC. 'Hits' on attack rolls represent attirtion of his hit points (which by RAW represent attrition of his luck, vitality, stamina, mental fortitude and the will to live) and not 'physical blows to his body'. Those 'hits' are
not him always getting physically struck by the giants weapon, and are certainly not him copping a 2 ton axe to the head and walking away alive.
He cant possibly know how many hit points he has, or how much damage the axe does to those hit points any more than an experienced cop 'knows' why he got shot at 20 times and walked away alive. It's not because the person shooting at the cop rolled a lot of 1's on the attack rolls (although it could be). It could also be a case that the shooter rolled really well to hit, reducing the Cop's hit points considerably, but the Cop is lucky, gritty, experienced and resolved enough in the gun fight to
not get physically hit despite losing a lot of hit points in the process).
Your character knows as much about how much damage a sword does, as that cop knows about how much damage a bullet does. He knows if he gets shot, he probably dies. He has no idea that he just got 'hit and his hit points reduced' (reducing his buffer of luck, experience and grit) several times, despite never actually taking a bullet.
Hit points are an abstraction of lucky and experienced dodges and parries and other events, vitality, stamina, resolve and grit. Youre treating them as meat. Which they are not.
He knows his luck and skill and toughness and will to live has in the past let him survive as they will now... He can take the hit by the giant then say "now remember that"
He may be roughly aware of his skill; his martial might is now enough to go toe to toe with a Balrog and survive. But he but he still knows that if that Balrogs molten razor sharp 20 foot long sword hits him, he most likely dies.
I don't understand what you are not getting... We both play the same game until you add a rule where instant death can acure. I just don't add that rule you do that is the entire idea of house rules you added something I didn't.
Youre playing a different game than I am. Best of luck to you.