Modern password management services are incredibly secure, with client-side encryption of your secrets, among other protective mechanisms (to guard against keyloggers, stolen computers, ...)
There is still a risk, because you're trusting third-party software (which in some cases is closed-source – including 1Password), but for most people that is a much lower risk profile than if they were managing passwords themselves.
For specifics on 1password's security, check out https://1password.com/security/
There lots of password managers that have had gaping vulnerabilities. From memory I'm sure I've seen LastPass vulnerabilities top HN just a while ago... yeah probably this one: https://www.bankinfosecurity.com/lastpass-patches-password-m...
FWIW I'm not a fan of keeping them in some cloud service dedicated for storing passwords (1PW's subscription offering, lastpass) because if someone is going to break into servers and steal passwords it's going to be from those fine people.
A middle ground is to use something like KeePass, where the encrypted password file is stored where you want it to be stored (ie your hard drive), where you can manage how you want to distribute that file between places you need it.
I still have to rely on the mobile app which isn't open source, but it is the recommended app from the main developer.
On the security spectrum, for the vast majority of people, a password manager is a step up in how safe their passwords are.
OP really cares about his privacy/security/password, but then he uses a secondary system to store it?
Is this the best way to do this? Break into the secondary system and everything is available. Keyloggers, eyes, stolen computers, all have the possibility of everything available.
I considered other solutions like written + put in a lock box in a bank, but thats really inaccessable.