So basically, Chrome is owned by Google They have an incentive to track all your browsing, not just your searches. Even if you aren't logged into the browser itself with your Google account, as soon as you log into Youtube, Gmail, or any other Google service, they can tie all of that back to you.
I don't know for certain that they are collecting this information, but it seems a pretty safe bet. Other websites will place cookies on your machines that allow them to know your browsing as well. Google themselves estimated that something like 60 companies can probably see more than 90% of your browsing history. So browsers like Brave (or Firefox configured correctly) prevent as much of this tracking as they can. It's always going to be a tradeoff between privacy and security though. Brave is probably going to be easiest for most people because it's pretty good without having to mess with any settings.
DuckDuckGo is helpful for not letting Google see what you're searching for, but that's only one piece of this privacy mindset.
Just to be clear, VPN companies have often marketed themselves very well, but I would say that most people don't have a need for a VPN, nearly every site is secure (https/encrypted) so the VPN isn't for security.
"Using a VPN will not keep your browsing habits anonymous, nor will it add additional security to non-secure (HTTP) traffic." -- privacytools.io
If you access Amazon on a VPN, Amazon can still knows who you are and what you're buying. If you access YouTube on a VPN, Google still knows who you are and what you're watching. And if you're on Chrome and it's tracking you, it can still see all your browsing history. The one entity that doesn't know what you're browsing, is your Internet Service Provider. They just see all your traffic going to one server somewhere, and since it's all encrypted your ISP doesn't know what you're looking at. The other thing a VPN is good for is making another server think you're in a specific country so you can access content that is region-specific.
But in general, I don't think a VPN is really going to be useful for most people, it's mostly so your local ISP can't see the specifics of your traffic, but that doesn't stop Google from seeing it. VPN companies are really good at making people think it's a necessity though...
Appropriately, a channel I follow (Christian engineer) posted a pretty good video on privacy and data collection recently.