You need something that has a reasonable adhesion to the quartz/glass in order to form a good seal, it needs to be workable into rather thin foil, it should be weldable, withstand working temperatures when forming the seal and withstand temperatures needed to form the seals. Plus it should not be prohibitively expensive material. Plus it should not be that hard, it should allow (preferably elastic) deformation without needing that high pressures
The cross section needs to have high aspect ratio between width to thickness. Because the trick is to redirect the expansion into the foil thickening, instead of widening, without creating excessive forces to crack the quartz. So then the quartz walls just have to slightly flex out, to create the room for the material expansion. And the thinner the foil, the less the quartz has to flex, so the tougher seal you can get.
"Feathered edges" are there to hold it in place, so the forces related to expansion won't move it and by that lose the adhesion and form possible leak paths. Plus because the thickness is never exactly even, any shift would mean stress concentrations on some spots, sp making it more likely to crack. usually normal burrs from the foil cutting are enough, it means the tooling is explicitely designed to keep them in place and not eliminate them (as is the aim for any normal sheet/foil metal processing).
Gradual seals (so gradually transitioning from one expansion coefficient to another to distribute the expansion) is a technique that was (and I guess sometimes even is) used in lamp making. But it is quite complex process, a lot of steps, so not that much compatible with high volume production. So generally it is avoided whenever possible. And with quartz it is possible...