Privacy

You really don't. And probably shouldn't. Remember this is the findings of a pen testing company that was working with these password managers. They found some issues. Issues that are very hard to pull off - you need the password manager servers to be completely compromised. Which is not something that happens often if at all. Vastly more common is just data exfiltration which bitwarden is secure against. Additionally the issues have already been addressed, in bitwardens article linked in that one:

All issues have been addressed by Bitwarden. Seven of which have been resolved or are in active remediation by the Bitwarden team. The remaining three issues have been accepted as intentional design decisions necessary for product functionality.

So you are already safer then before without having to do anything. Switching now all you are doing is switching to a provider that has not undergone this testing and may or may not have similar issues.

Don't just jump at the first mention of things like this. You really need to look at the companies response - like Lastpasses who have given a token statement that basically says they are not going to fix these issues any time soon if at all. Stay away from companies like that. But companies like Bitwarden that actively fix issues that are found are worth sticking with.