Exact, the metal wires are just embedded into molten glass which is subsequently cooled down. However, not all metals allow this. If a system free of leak has to be prepared, for example a lamp, the expansion coefficients or metal and glass should be very similar. Depending on the glass, the best metal or alloy therefore needs to be chosen with extreme care. Otherwise for sure a microleak will occur after cooling. As far as I remember, for example, tungsten is one the best for being included in borosilicate glass.
Dealing with borosilicate glass to tungsten seals, a good book reference is: J.H. Moore, C.C. Davis, M.A. Coplan, S.C. Greer, "Building Scientific Apparatus", 4th ed., Cambridge University Press, 2009, pp. 89-90 and 132. Considering other (more or less) compatible metals or 'kovar' ─ Ni–Co-Fe alloy compatible with the thermal expansion of borosilicate glass ─ you may refer to a few selected internet sites (e.g.):