There is some truth in all that has been said, including
@winston1 but the problem is the lighting industry is it seems unable to label or give useful specification for their products,
this company specialises in 12 and 24 volt DC lighting however in the main lights bought from high street shops are either 12 volt or 230 volt AC.
The problem is even if this toroidal transformer
is ideal to comply with 50 Hz 12 volt AC supply, it can't be used with a dimmer switch, and at £19 is not cheap rated 50 watt. The 0 - 50W you selected will likely work OK, but the
likely is the operative word, the kHz range of output could turn the set up into a mini wireless transmitter if the cables happen to hit the right length for the frequency. Also dimming any electronic lamps can cause problems where the power supply/driver/transformer/ does not match the switch, specially where the switch does not require a neutral, and this includes both 12 volt and 230 volt lamps.
You should not dim quartz lamps so likely no problem using a
toroidal transformer this is how I would do it, but I have a 200 watt toroidal transformer spare, so don't need to spend £50 on a new one. I have some G9 bulbs 4 x LED and 1 x quartz, in the same chandelier and lucky you can't tell which is which, and that is likely the easy way to move to LED leave one quartz in the circuit. However you seem to want a very high colour temperature, I have never considered quartz lamps to be yellow, I have always considered them to be if anything too white.
So maybe something wrong to start with?
LED is a DC current dependent device, but in the package of a bulb they are often designed to work on AC at a fixed voltage, and to do that the AC needs to be made into DC and some current limiting device added. One would hope the rectifier in 12 volt versions would take either AC or DC but there is nothing on most bulbs to say that, I have mainly LED lighting in the house, only two have ever failed, one replacement LED tube for a fluorescent lamp, and one G9, but at £5 for a bulb one does not want too many failures, so with the power supply you linked to and the one
@winston1 linked to you are taking a risk, they may work, or it could become a transmitter or could over load the rectifying diodes, as put DC into an AC bulb and double the average current goes through a diode in most cases.
If you have access to fit the larger toroidal transformer I show then I would use one of them, but if the transformer is to fit through the hole where lamp fits, I would take a chance and fit the one you linked to in your first post. There is no right or wrong, just shades of grey.