..The center drill drills into the bar about 2 to 3mm then goes blunt as if the steel has gone hard again .
Cheap Chinese centre drilsl will do that. Combination of mediocre quality high speed steel and poorly ground cutting lips.
You don’t need to use a centre drill to start a drilled hole anyway. Common modern practice is to use a stub drill instead. In this case, such a small diameter hole to be drilled, I use a much larger centre drill as a stub drill. You use just the very tip of the large centre drill to make a small divot in the job, say 2mm diameter by maybe half a mm deep. Just enough to guide the tip of you regular drill bit when you start to drill the actual hole into the silver steel. That is all you need in this instance. Then drill on through with whatever regular drill bit you need to use.
If you start with a fresh piece of silver steel as supplied that has not been heated up etc. you should have no trouble drilling it with the above method.
If you are playing around hardening or annealing silver steel, note too that “cherry” red refers to the very dark red that cherries were back in blacksmithing days and not the bright red of the cherries your girlfriend gets in her cocktails today.
And another way of slowly cooling red-hot steel to soften it is to bury it in a bucket of powdered lime while it is still glowing red.
But as has already been said, you would be better off starting with a fresh piece of silver steel and machine it in as-supplied condition.