I'm afraid this may be a real mess, and dangerous
The problem is you have 2 hots fed by 2 separate circuits, fed by a common neutral. This configuration is called a multi-wire branch circuit or MWBC. There is nothing wrong with these, but they need to folow special rules to be safe - and yours don't.
The single most important thing is they must be on opposite poles. There must be 240V between the two "hots". That is the only way the circuit can avoid overloading the neutral. Experience has shown careful breaker placement is not reliable, because people move breakers around. The modern rule is to put the circuits on a 2-pole breaker which is designed for 240V. Then, the panel's design will assure you place the two hots on opposite poles.
You identify problem MWBCs in the panel by looking for 3-wire cable (black red white) whose black and red wires do not already go to a 2-pole breaker.
Because two hots share a neutral, neutrals must be pigtailed like grounds are - and for the same reason: removing a device must not break the wire for downstream loads. If you tried removing that receptacle right now, you would be shocked when you tried to remove the neutral wires, by the current flowing down the other circuit. This is the other reason to use a 2-pole breaker - it assures when you shut one off for maintenance, it shuts both off.
Once that's fixed
It looks like we are joining this MWBC "already in progress". The red wire carries switched-hot from one leg of the MWBC... And the black carries (presumably) always-hot from the other leg.
So get a short stretch of /3 Romex cable, because you need to make some pigtails: first to the bundle of blacks, to get an always-hot for one side of your outlet. Then don't forget you need to pigtail the neutral.
Don't break off the tab on the neutral side, and connect the neutral pigtail to that.
Do break off the tab on the hot side, and connect the black pigtail to the unoccupied side.
I would continue to ignore the red pushed into the back of the box, since we know nothing about it.