Here are two photos of the same painting:
I have seen in museums how dark old paintings can be, so I guess the leftmost version lies a little less. The rightmost is sweetened. It's adjusted for full brightness range coverage and subjectively good looking colorfulness. The contrast increase causes increase of color differences and saturation which has been compensated by reducing the saturation and apparently by recoloring the blue cloth. Quite far from the truth, I guess.
You must decide how much you want to sweeten those images which look a little dull on the screen. Ask the payer of the bill.
If you want to stay as truthful as possible (all real world colors are not possible in RGB screens) take two photos of every painting with exactly same light and camera exposure (use manual mode!). The first image has the painting as is and the other has a partial reference overlay image which has at least a piece of black, a piece of white and a piece of 50% grey. It preferably also has some painted colors. It can contain a small painting.
You adjust the photo in your computer so that the reference looks as truthful as possible without causing too much unwanted effects to the painting. In Photoshop there should be no difficulties to apply the same adjustments to the referenceless photo. Learn to use Camera Raw, adjustment layers and smart filters.
Be sure the reference doesn't cover the brightest nor the darkest area of the painting.
How to prepare the lights and set properly the camera is off-topic here, but at least have some lights, use a DSLR, have a sturdy tripod under it and shoot RAWs, not JPGs. Make all possible to keep glaring reflections away. I have used polarizing filters and used TFT displays as a source of polarized light. The resulted long exposure was possible due the sturdiness of my tripod and timed camera triggering.
If your photos must contain a piece of gallery wall, you can insert it afterwards to keep it consistent.
There can be some reason why you cannot use extra lights. In that case place a BIG grey paper in front of the painting to get a map how the light is distributed. You can compensate the uneven light with it in Photoshop. You can also fix the white balance with it in Camera RAW. Now all your examples look too yellow. In addition they have much camera noise which appears as random colorfulness on the wall.
Here's a totally subjective attempt to fix your leftmost example. It seemed to be the least overexposed version in the bright reflection area on the wall:
Without a reference the result cannot be reliable, it's a guess.
User Stan suggested to use a color reference card as a reliable reference, He hinted that camera can distort colors due those wavelengths which are beyond the visible range but still seen by the camera. The problem is significant at least for those take photos of old paintings because some traditional color materials can reflect well invisible radiation. Color reference card can help to reveal the problem, but IR and UV filtering cures it.
Museums do not allow flashes because the send UV radiation. It detoriates materials, they do not care do your photos get the colors right. Led lights make UV internally but convert it to visible range with fluorescent materials. I have seen writings that they can still leak some UV like fluorescent lamps. One example: https://www.premierltg.com/do-led-lights-produce-uv-led-tanning-beds/. Unfortunately I cannot say does the leaked UV be a cause for wrong photo colors or a reason to kick you out if you try to use LED lights when you take your photos.