Can a VPN really protect you on the LAN side?

Context: at work, we have to engage with these ridiculous AI-generated cybersecurity videos, then take a very simple 3-or-4-question quiz to prove our security compliance for the month. Frequently, I find that these videos make outrageous claims. Once, one video made a claim that everything you download from the Google Play and iOS App Stores are completely safe, despite stories like these appearing all the time.

Anyway, the videos we watch frequently make claims that, if you're on public Wi-Fi, that you must use a VPN, because it obfuscates your devices and traffic from hackers that might be sitting on the network. My question is, does a VPN really protect someone on the LAN side? To my limited knowledge of VPNs, they don't hide your traffic on the LAN, just the outgoing WAN side when the tunnel punches out. It may help with some MitM attacks, according to this article, but I'm not convinced that a seasoned hacker couldn't find their way into your device or accounts, even on a VPN, through the local network.

Sorry for the word vomit. I'm also procrastinating!