The simple answer to your question
"Is there an idiom [regarding the ineffability of art, the difficulty or impossibility of explaining the real nature of an artwork] ?"
The simple answer is
Idiom has an actual meaning (check dictionary). You should note that you would be severely misguided if you considered one of the (many valuable and astute) quotes mentioned in this QA, as anything like an answer.
Be aware that on SWRs, it's completely normal and commonplace on this site that the correct and only answer is
A particular danger is that non-native speakers reading here, can be misguided by "hopeful" answers on SWRs where in fact the answer is "No".
One word that may help is "experiential". If you assert that Bladerunner is experiential, or that standing in front of Flammable by Basquiat is experiential, or that Dancing Queen is experiential, you're essentially asserting that concept: that it is ineffable, and only the experience is meaningful, you can't use words (ie, it is ineffable).
However, exactly as JonathonZ points out below, "experiential" is a bit obscure / specialist / arty-farty.
"it must be experienced" or
"the experience can't be put in to words"
are the sort of constructions that are what you are getting at.
But please be aware they are exactly not idioms.
An idiom is a group of words established by usage as having a meaning not deducible from those of the individual words (e.g., rain cats and dogs, see the light).
A phrase like "it must be experienced" or "I am walking" or "that's a house" are not idioms, they are phrases.
OP is asking for an idiom (like "raining cats and dogs"), and there is no idiom. So various folks have helpfully supplied simply "sentences that may explain the issue in question" (as I have). But it's really important to realize those aren't "idioms", they're just the usual (often extremely confusing) "there's no idiom but here's a suggestion / invention / alternate discussion by me" material seen ubiquitously on this site in reply to swrs !