Because I'm actively researching this topic, I'll put all of my thoughts in this temporary answer.
The crafts of goldsmithing, silversmithing, and brownsmithing (coppersmithing) would be closely related to the manufacture of these sorts of implements. Techniques involved (and still found today) include:
- Rolling (manufacture of sheets)
- Wire-drawing (manufacture of wires)
- Wrought work (forming)
As seen here, candlesticks can conventionally be made by casting in a foundry. They can be made by hammering techniques as well if the design is simple enough. They are often made in separate halves, which are then soldered together and polished.
Very high quality implements can be made by raising and soldering alone. This is shown by videos such as this one. From the same channel, silver pieces made in parts are also shown, like this. Other techniques in silversmithing that are still technically within the 1800's timeframe can be found in Gee's The Silversmith's Handbook (1886). Here, more specific tools such as the sparrow-hawk, and the snarling tool, are described. Other techniques mentioned include swaging, dooming, spinning, and stamping, which is cited as coming into general use around 1851.
Fastening of elements could be accomplished by e.g. soldering, riveting, pinning, etc, and threaded fasteners were mass produced beginning in the early 1800's. These methods have not changed dramatically. This is relevant as e.g. a rivet appears to be used in the third "chamberstick" shown in the question.
When classical methods were inconvenient, or when mass production is needed, hand-tools are replaced by machining tools. Lathes powered by steam, water wheels, or even horses, were available and used for turning as one would expect. Metal spinning would be a particularly appealing choice, which grew in popularity towards the end of the 19th century; very nice implements can be made with this method to obtain common axisymmetric shapes. A great example of silver candlesticks being made with spinning in a simple way is shown here.