As an "expert viewer" of Baumgartner Restoration, this site usefulness is questionable. If you look at those color palettes, most of them brownish that is because of dirty & old oxidised varnish. These are not the intended look of these paintings. So these color palettes has nothing to do with those 3000 masters. https://youtube.com/@baumgartnerrestoration
Generally, a painting is best viewed and photographed in as close a lighting environment as it was painted. I have seen many paintings 'blasted' by unnaturally bright gallery lights. There is a reason why a gallery lighting designer is a real job. However, in my experience effective gallery lighting designers are as rare as rocking horse shit.
It is true that the paint the artists applied many years ago will often bear little resemblance to that which we now see. This is less true of earth browns and very true of paintings done at the beginning of the pigment revolution, when wonderful colors were produced which were later discovered to be very 'fugitive'. However, the relative relationship between these paints remains more or less intact, and IMHO this is the most important factor in aesthetic evaluation.
Another factor is how a photo flattens such differences as rough vs smooth (and their consequent light reflection properties). In a Titian painting, huge areas are untouched rough red oxide primer on rough canvas, vs the slight gloss of oil paint. Importantly, old masters would often apply their lights as (smooth) thick paint and their dark as thin glazes (or scumbles) above a thin primer (red or green or yellow ochre or whatever). The frisson between these layers gave the darks their depth that they would otherwise have lacked. This is mastery of dynamic range at its finest. Googles art project photos comes close to capturing this. For an example, check out any portrait by Durer in Google art project.