In a pure technical standpoint, directly answering your question: yes, Linux is a free and open source kernel, and most(looking at you Ubuntu.... Damn you) Linux distros are privacy respecting, so it is a good choice.
Going a bit more beyond: it depends. Do you want full privacy? Or just peace from Windows?
If you want peace from Windows, yeah, Linux is a big step-up, but it works and once you get the hang of it, it's a bit hard to go back.
If you want privacy, just switching to Linux will help, but not solve. That's a entire separate journey you'll have to take alongside your Linux escapade.
What softwares do you use? What services do you use?
If you use Microsoft Office, you'll have to switch as that both doesn't exist in Linux, but also is kept by Microsoft which.... You know how Windows is.
If you use Google anything, you gotta seek to de-google. Replace Google Docs with Nextcloud, replace Google with some other search engine, switch to a privacy respecting browser, etc.
Do you use some password manager? How safe are those? And what accounts do you have? What's your mail provider?
There are thousands of little questions you'll have to make yourself about what you use and what you do. And then, privacy nowadays sadly is a balance.
The more privacy you have, the more convoluted and less practical it ends up being. Setting up and using something like KeePassXC is a lot less practical than just hitting save in Google Chrome to save into your Google account.
Full 100% privacy isn't feasible for a normal person, and that's okay. The small percentage that "leaks" out is so small, it gets lost in the bulk collecting of data. At one point you'll need to figure out how much convenience and practicality you want to give up on for privacy.
And without loosing much of it, having just a few small tweaks, boy you can go far. I have de-googled completely, switched 99% of my services and softwares to privacy ones, even rock Alpine Linux. And it still feels extremely practical and easy for me. You just gotta weight and figure out what works for you.
EDIT: cuz my wording was a bit off, this isn't to discourage you, by opposite. It is more of a informative for you to study exactly your use case and how you want your privacy to be. Privacy is subjective and depends on the context, so there's a bit of homework involved with it
From my experience with Splatoon... Anyone with the name of 'goggles' is a menace that should not be trusted. Make sure to keep your distance and a eye on your back, in case the menace decides to expose your pants off