The aforementioned managers are only as secure as you make them, keepass and lastpass are not cloud based, as stated before, they are non custodial and the data is stored on your PC.
I'm pretty sure LastPass is actually cloud-based?
KeePass is great and doesn't store anything anywhere (other than in a file on your PC) unless you download an specificy plugin to make it sync with cloud storages (Drive, Dropbox, etc...). But Lastpass is fully online.