The answer is actually yes if you're willing to wait.

Interstellar travel is not impossible, no matter what anyone tells you. We know how, it's just wildly impractical. We've barely even left our own planet, and we've managed to throw a few chunks of metal out of our solar system so far. We lack the industrial capacity to build an interstellar ship, we do not lack the physics.

Yes but none of them are especially pleasant. The least unpleasant way would be some kind of photonic rocket as it gives you the highest possible exit velocity and thus efficiency. Matter - antimatter annihilation produces photons that can be used for this. Antimatter collection and storage is an issue, engine and ship design is an issue, radiation is an issue, in space construction is an issue. But plausible? Sure, I guess. The ISVs from the Avatar movies of all things are the closest to what this would look like.

Well, even if we could not reach such a planet in a reasonable time yet, a research like this could still be very useful for many reasons.

It could help us learn how our habitable environment works and operates, it might be applicable for terraforming or habitat construction.

There is also a non-zero chance of some sort of life, possibly intelligent developing in such an environment (as proven by our sample size of 1). That life can be active at the moment (from our PoV - light speed and all) or was active in the past, so we should look for bio signatures or even signs of mega scale engineering.

Generation ships with plasma sails, probably.

Yes, easy assuming multi-generational arcologies.

There are plenty of designs that get you to 0.1c or above if you are Kardashev 2, things like light sails powered from the Dyson sphere.

Nothing plausible for anyone living today AFAIK.

It wouldn’t be that fun to live on one. The article says picture paradise, but we’re talking about potentially 1.5-2g with a dense atmosphere; we’d feel terrible all the time. Also whatever biology is in that planet is probably not compatible with us; we likely wouldn’t be able to eat it. Finally once you land, you’re screwed and stuck there. Traditional chemical propellants barely work for our planet, we’d need new ways of taking off for higher escape velocities.

We are at least 1000 years away from being anywhere close to this.

Sure, just not the same human that launched from Earth.

The Cologne Cathedral in Germany was started in 1248 and finished in 1880. That's 632 years.

>given what we know about physics at the present?

No.

My hypothesis has always been, hey, have enough kids out there, and sooner or later, they'll learn enough about the physical sciences to at least explore far away worlds. (If not go there in person.)

But yeah, expecting we can get there with what we currently know is a bit naive. We need to, <gasp>, horror of horrors, fund more research.