Both of the kit lenses can be considered "all-purpose" lenses, just in different ways. Kit lenses are usually lower-cost all-purpose lenses. That's why they come in the box with the camera.

But let's turn this around and look at this from your smartphone experience.

On a smartphone you typically have three back cameras you use for taking photos: an ultrawide (0.5x zoom), the main lens (1x zoom), and maybe a telephoto option (3x or 5x zoom).

All of these lenses are "primes"; that is, lenses that don't actually change focal length or zoom (zooming on most phones is done by resizing/cropping, aka "digital zoom"). And most phone cameras have a maximum aperture (how wide the iris in the lens can be set) of around f/2.

The general equivalency of the main lens is 24mm, so all the #x zooms are relative to that. So, an ultrawide is roughly 12mm-equivalent, the main is 24mm-equivalent, and a tele is say 72mm (3x) or 120mm (5x).

But we can't compare these equivalent focal lengths (what those focal lengths were frame like on a full-frame or 35mm film camera) directly to focal lengths of lenses used for a Z fc, because the Z fc uses a smaller APS-C sensor with a 1.5x crop factor.

So, if we look at the two Z fc kit lenses:

Z 28mm f/2.8

This will frame at 28*1.5 => 42mm equivalency. Or similar to a 1.75x zoom lens would on your phone. It's sort of midway between the main and a 3x tele lens. At f/2.8 max. aperture, it's a stop slower than your phone lenses, but still fast enough for shooting handheld indoors without a flash. It will also let you blur backgrounds for portraits a bit more by giving a thinner depth of field (how much of the scene is in focus front-to-back).

This is, essentially, a "normal" fast prime that's not particularly wide or particularly tele. It can be used for walkaround shooting and portraits. It may be a little tight for landscape shooting or selfies, but you can use it for both.

Z 16-50mm f/3.5-6.3 VR

This lens actually zooms, with 16-50*1.5 => 24-75mm equivalency. So this can basically cover everything from the 1x main lens on a phone camera to a 3x tele lens with a continuous optical zoom range. It's more versatile on framing choices than the 28mm, allowing you to vary between both wide angle and short telephoto.

But the max. aperture of f/3.5-6.3 (f/3.5 at the 16mm wide end, and f/6.3 at the 50mm tele end) is slower than the f/2 of a smartphone lens, and may require noisier high ISO settings to shoot indoors handheld without a flash. It does have VR (vibration reduction) stabilization to help keep camera shake blur from handholding happening at lower shutter speeds. But it cannot help with blur from subject movement. Only a faster shutter speed can do that.

So which one is more "general purpose" depends on how you define "general purpose". Do you want more flexibility in framing (focal length)? Or in the light conditions you can shoot in and depth of field (max. aperture)?

As a last note, while body-only packages of the Z fc appear to be out of stock at the moment, if you wait, it is likely to come back into stock or possibly be replaced with a newer model. But "body only" packages typically aren't for a first-time mirrorless owner to pick a lens a la carte, as much as they're for someone upgrading bodies not to be lumbered with YA kit lens.

When choosing your first lens, you are in something of a "chicken and the egg" dilemma: to know which lens you want, you need experience with lenses. A low-cost kit lens can give you that experience and a point of reference to figure out what it is you want in a lens in terms of focal length, max. aperture, or other features (focus motor, stabilization, macro capability, etc. etc.)