No using a VPN doesn't hide your "user agent". A VPN generally just masks your IP, leaving your user agent HTTP header untouched.
I guess you can get a user agent switcher software, or browser extension but I have not tested this. I recommend using brave browser, which by default blocks MOST browser fingerprinting by default. Not to mention, Brave just announced recently that they will be offering VPN and firewall services for a modest 10$ a month. Not only does this protect your browsing, but protects ALL traffic on your phone.
Remember, Proxies are a bit different than a VPN but pretty similair. Both connect you to another server and forward traffic from there, but a proxy is only capable of handling web traffic, where a VPN is able to handle your entire internet connection
Privacy online is definitely important. Because do you know that moron "Gimpy" goes on the Horror Film Wiki and edits every damn page I've ever interacted with, with prior aliases?
Some people on an autism forum are concerned he may be a fruitcake, after I described what he was doing on other forums over the last 3 years. And no, I don't mean the fruitcake with sultanas and cherries. But you know? An actual obsessive madman that cannot take a hint.