Short answer: if you have YouTube Premium, its built-in offline downloads work fine for casual use inside the app. If you want an actual file — to keep past 30 days, move to another device, or watch without an active YouTube app — use the extension's YouTube panel: paste the link, pick a quality, download the mp4.
YouTube does have an official offline feature — but it comes with real limits worth knowing before you rely on it:
That's a fine trade-off if you're a Premium subscriber who just wants to watch on a plane and reconnects regularly. It's the wrong tool if you want a video that behaves like, well, a video file.
Only save videos you have the right to keep a copy of — your own uploads, ones licensed for reuse, or ones you're downloading strictly for your own private, offline viewing. This pulls from what's already publicly playable in your browser; it doesn't unlock anything private or region-restricted.
Very long or very high-resolution videos can produce a file over 2 GB, which will fail at the storage step — if that happens, retry at a lower quality setting rather than "best." And this only works on videos that are already publicly playable for you in the browser: private, members-only, or region-blocked videos will fail the same way they'd fail to play normally.
Because building the file takes real server time and bandwidth, YouTube downloads are metered by the finished file's size — see pricing for the traffic-pack rates. Failed jobs aren't charged.