You solder the chains (even the smallest ones).
There are 2 types of chains:
1. eyelet
2.links
eyelets:
you must connect before soldering
always 2 links together (like a circle in a circle, you have to manually put it together with tweezers), place such a complex chain gently on a fireclay plate, or on a charcoal plate, brush the surface to be joined with a brush
with a soldering iron (borax dissolved in warm water), then apply with a brush
pellet (the bundle is a miniature piece of solder, fitted to the size of the solder spot, typical is 1x1mm flat).
Then you gently heat the soldering area with a torch as the solder "grows" and the solder may "pop out".
When water particles evaporate from the solder, then you heat the soldered place with a stronger flame (with more air), you do it with a pulsating motion, slightly moving the burner nozzle away and bringing it closer, because too strong a burner flame can stiffen the cells next to the soldering point.
If the chain is really small, then unfortunately you are not able to solder only 1 link and rigidly solder 2 neighboring links, but this is such a precise work that you cannot see it.
links:
you need to on the fireclay plate, arrange the 2 ends as close to each other as possible
(In general, the rule is always this: the more carefully you assemble 2 pieces to be soldered, the easier it will be to connect them with solder).
Then you do as with an eyelet chain.
I know it sounds difficult, but it's all a matter of practice.
The goal is to connect the 2 pieces so as not to stiffen the rest of the chain.
For soldering, I use a typical propane butane gas gun torch.
After soldering, you do not grind anything, it is a fine point, almost invisible.
All you need to do is clean the soldering area
stain (the stain is a 10% solution of sulfuric acid or acetic acid, which frees the solder point of dark metal oxides formed during heating with a burner).
You wipe with a cloth and it's ready

ps.
A colleague in the link above gave the contact information to the art store. there is an interesting device there: the PUK3 micro welder works exactly like a typical welding machine, allows you to connect the elements without too much heating, the only drawback is the price of about 10,000 PLN.
Regards, WO