Overall not a bad tweak from the RAW Assassin, but I wonder if this is too OP:
Level 3: Heart Seeker
You can make an attack that pierces through most defenses. As an action, you can make one attack with you a weapon with the light property. Treat the target's AC as 10 against this attack, regardless of the target's actual AC.
During the first round of combat, if you hit a creature that has no yet acted with this feature, the attack is automatically a critical hit.
At higher levels, it makes hits practically guaranteed, once you have a +9 or better on your attack roll (not hard with magic items, etc. you could have this before tier 3).
Maybe bump the AC to 15 instead of 10?
Level 17: Death Attack
When you score a critical hit on a creature, it must also make a Constitution saving throw (DC 8 + your Dexterity modifier + your proficiency bonus) or falls to 0 hp. On successful save, the creature is stunned until the start of its next turn.
This is also a bit strong. If you have elf crit fishers you could get crits nearly 15% Do a 3-level Champion dip to crit on 19s as well and it jumps to over 27% Granted, you aren't getting it until 17th level, so maybe it is fine....
You could also do something like this:
Level 17: Death Attack
When you score a critical hit on a creature
using your Heart Seeker feature, it must also make a Constitution saving throw (DC 8 + your Dexterity modifier + your proficiency bonus) or falls to 0 hp. On successful save, the creature is stunned until the start of its next turn.
This way, it isn't ALL crits, just the first one before the enemy gets to even act?
I still think having Assassin as a background is the best solution, though.