congratulations on your pix, these are much sharper and have good background contrast - it's always difficult to see details clearly when people include their washing hanging in the garden, or a collection of kitchen utensils
See what you mean about the join - can't be certain of what happened here...........if the guy had first cut the facets on the stem then broken it but wished to re-join the two pieces, he'd still have the same number of flats on each piece.
If he hadn't cut the facets before re-joining, then when he did so much of the join would have been obliterated by the cutting - so as you say, it's mystery.........let's hope someone else might have the answer
Ordinarily, facets on stems are cut at 90 degrees to the axis of the stem, so cutting can get very close to any join - can only think that your glass was a botch repair.
Attached are three pix of my drawn stem wine.........this shows the unusual 'twist' to the stem, which doesn't appear to be a join, so must be decorative and whilst it would be assumed an easy job whilst the glass remained plastic and before cutting the stem facets - it appears the twist was made after the cutting, since the facets themselves can be seen to have twisted. the black marks are where I ran out of fingers whilst counting the number of flats.
Wineglasses, usually, are made in three parts.........bowl, stem and foot - that is except the drawn stem variety which are made in two parts only.........bowl/stem and foot. However, I think that my example might possibly be an exception to the rule, and looks as though it could be bowl/stem with twist - lower part of stem with the 'nut-shaped' knop - and finally the foot. I could be wrong, but it's certainly an unusual glass, albeit attractive with vine and leaf engraving, lead construction with stunning ring. Because of the unusual stem construction, I'm not entirely sure how to date the glass, but might take a gamble and say c.1820 ish - foot is certainly wider than the bowl.
Polished pontil depressions, on their own, are unreliable for dating - they've been a feature of quality glasses since c. 1770 and well on into the C20 - so we need to combine other features for dating.
Much Georgian glass is not simple - you'll see when you get a good book. Knops, bowls and stems are classified into groups, and although I could be wrong, this bowl shape is not from that period - I'm also doubtful of Georgian in view of your comment that the bowl is thick.
Even with the pontil depression and cutting my opinion is that this glass, like the other one is second half C19, albeit better quality.
On Georgian pieces, cutting proper is confined more to stems rather than bowls - it was the Victorians that were obsessed with cutting everywhere.
You might consider buying/investing in one or two Georgian glasses that will show features that will show clearly the difference between 1790 and 1890 - colour is not always easy to describe either.
You've made a start - and you can now go around flicking everything you see - tell people you're looking for seeds and striations and discuss foot to bowl proportions like an expert