I can see Eddie easily rationalizing only killing Peter because he sees Peter as a threat to everyone. He's a narcissist dodging self accountability by drowning in self pity, the exact opposite of Peter. Who therefore who thinks that Spider-Man ruined his life and deserves to be terrorized because he might have acted like a dick a couple times while wearing the Symbiote.
So it's not a leap to imagine that Eddie would therefore think Spider-Man harms EVERYONE ELSE's lives too, or at least eventually will.
Because everyone knows Eddie Brock is an innocent upstanding citizen who got dealt a bad hand. Of course. Everyone loves Eddie Brock. Like the employer that fired him. Or the girlfriend that left him. Or the abusive cop dad that saved him from a drunk driving manslaighter charge but smacked him when he wanted to confess and serve his time. No one has it as bad as Eddie.
Eddie can never stop feeding his ego, reigniting his delusions of grandeur fueled by hated for Spider-Man. Because then he has to look in the mirror and realize he's as much of a monster internally as he already looks externally. And thus confront how much he actually hates himself for ruining his own life.
But hey, give him some credit. He knows what Peter Parker is "really" like, through a mere few brief casual interactions as co-workers. And everyone is else is just too naive to see him for the menace he is until it's too late. You're right to think that he's also hurting Peter's loved ones indirectly too, but he would just say he's "saving them" from Peter or some self righteous nonsense.
Eddie's vendetta makes as much sense as why J Jonah Jameson hates Spider-Man, which always has different interpretations that range from petty envy, to Spider-Man taking attention away from his son the astronaut, to irrational insecurities fueled by trauma, to a marketing stunt for selling newspapers, to Peter sharing some blame by stoking the fire by mocking him in retaliation.
And let's not even get started on what makes Lex Luthor hate Superman so much or why Joker loves Batman so much he wants to break his no killing rule which would somehow proves he's right. Supervillains tend to be crazy. But often have a method to the madness, which makes them compelling.
As much as I didn't care for the Venom film, it hit the nail in the head in calling Eddie Brock a loser. Because that's what he acts like. A sore loser.
What irks me about Venom is when he harms other people besides Spider-Man. Because then Eddie loses his supposed moral high ground against Peter "ruining" his life. That's the one flaw that bothered me about Spectacular Spider-Man's Venom targeting Aunt May and Gwen Stacy despite loving Eddie's buildup from being Peter's older brother figure to to becoming a tragic villain. He's easily the most sympathetic take on Venom who isn't just a delusional jerk before AND after meeting Spider-Man. So he loses his depth as an antagonist and just becomes another homicidal villain. Or just an idiot.
But no, his 90's redemption doesn't make sense. Many comic book redemptions don't make sense and aren't written well. They're only done because villains turned anti-heroes is a popular gimmick. Which only makes the Punisher look like an imbecile because the Avengers and X-Men are chock full of former murderers and supervillains.