It's the wound strings rather than the plain strings that are the weakness of the Artist strings.

OK, so buzzing near the nut and on open strings could be several things.

1. The neck relief is a bit too flat and you need a bit more bow in it. Very few necks have an equal amount of bow on the treble and bass sides, so if you've only checked the bass side (as its the side nearest you when playing) then check the treble side as well.
2. The G string saddle height is a bit lower than it should be (maybe the notch is deeper than the other saddles). As you can't adjust individual saddle height and the G string is almost in the middle, the bridge needs raising slightly on both sides.
3. There may be a high or humped fret above those low frets that the string is catching on
4. The G nut slot may be poorly cut and the string is buzzing in that. A too-low G nut slot would only affect the open string if that was the only issue; fretted strings should still play fine, but if the nut slot is cut so that it slopes from the headstock side down to the fretboard side (instead of the other way around), then the open string can certainly buzz in the nut, and you can sometimes hear buzzing from it even on fretted notes.
5. You can sometimes get buzzing from the saddle itself if it doesn't sit well in its channel or the notch in it doesn't suit the string, and this can appear to come from the fret. Sometimes just tweaking the intonation screw can cure this (some screws are slightly bent so will raise the saddle off the bridge and then lower it again as they are turned). Sometimes a rub of folded P400 grit paper in the slot helps.
6. Check that the tuner nuts are tight. They can come loose under playing vibration, and then the washer can rattle against the nut, though this tends to happen playing all strings, not just one. But it's a good idea to get a spanner and tighten those nuts from time to time.

It can of course be a combination of two or more of these things. The G string nut slot may be too low, which is why the open string buzzes, but there may be insufficient neck relief or the bridge needs to come up as well to cure buzz on the other fret positions.

I'd start by first looking at the G-string slot height, then the neck curvature and then the string height. The guitar hasn't been played for a while, so with the wood adjusting with temperature variations, the neck relief and bridge height may simply need tweaking.

If they all look fine, then best to get back to basics and check for high frets. Get or make a notched straight edge and a fret rocker if you haven't got one. Take the strings off then get the neck straight with the truss rod, using the notched straight edge to make sure the neck is straight.

Then you can run a straight edge along the top of the frets to look for any obvious gaps. If nothing is obvious, then check with a fret rocker. It should cover three frets so that if they are level, you can't move a fret or see a gab between it and the middle fret. A high middle fret will allow the rocker to rock. I'd check on the bass side, middle and treble side of the frets a syou can get frets with a different curvature to the others.

High frets you can first try tapping down with a soft-faced hammer (or a hammer and a block of wood) as sometimes they will seat better and the problem is solved. One or two high frets can be dealt with on an individual basis, and you may only have a high bit in the middle. If you don't have a fret profiling file, you can try just rubbing down the high section with some wet and dry paper. Mask off the fretboard around it first to protect the wood. Then I'd rub along the high part of the fret with P240 until it's level, then go up through the grits, a few strokes on each until its fine enough to polish with metal polish.

More than a couple of high frets, or just some low frets and you are better off doing a full fret level, (if you feel capable).

Thicker strings require more tension to get to pitch than thinner strings. More tension gives more of a concave bow to the neck (unless you adjust the truss rod to compensate), which raises the strings off the frets just that bit more, and so reduces buzzing. The strings are also supposed to vibrate with less amplitude (though I'm not 100% convinced about that myself) so again, they are less likely to touch the frets when vibrating.

It's very difficult to diagnose buzzing issues remotely. Apart from a low nut slot issue (fit a thin shim under the nut or fit and cut a new nut) they are normally curable by truss rod and bridge height adjustment. But that may give you too high an action, which is when you need to address the frets.