Let me give a bit more long winded explanation. LastPass has been compromised because it was the biggest password manager that was hosted on some big corpo's servers, therefore a massive fucking target was painted on the service, and after many years of shots fired, one managed to hit the critical spot leading to a full leak of data of millions of users.
That is not to say that all password managers are bad. Password managers that store your passwords on some server you have zero access to and do so for millions of people are bad because it's only a matter of time before it gets compromised because of how prominent this is.
Note that Bitwarden, by default, is no different than LastPass. You register on their servers, and save all your passwords on their servers. Therefore those servers can share the same fate as LastPass.
However unlike LastPass, Bitwarden is open source, and they offer a self-hosting solution, so that you can host all your passwords on your own devices that you have access to. This also means that your private server will be less likely to be hacked simply because barely anyone will know of it's existence.
As for what I use and I find the best option for me, that would be KeePass, as all the passwords get saved in a single file on your computer. Then it's up to you how you want to synchronize and backup the said file, and there are solutions for it that will allow you to do so without ever using the Internet to do so.
For example Syncthing after proper configuration will only synchronize files in your local network, and if you happen to know and are able to set up a VPN connection to your home network, you can synchronize your files wherever you are through a private, encrypted tunnel that only you have access to.
Hell, you could even use something like Dropbox and it would still be infinitely more secure than LastPass, as there is no big target on DropBox as the place that stores passwords, and if your password database got leaked, and you weren't a mongoloid and used a strong master password or even some form of 2FA, the hackers won't be able to compromise it anyway.
However do note that this means how you take care of your password database is up to you. You can fuck up and lose all the copies to it, losing all of your passwords. But if you're not a complete retard, you'll keep them safe, you'll have access to them, and you won't ever get compromised. But this is a less normie friendly method due to how much depends on your know-how of how to keep your shit backed up and safe.