Some immediate progress we can make without Light Show is to identify the relevant languages and use that to help us interpret the initial flavortext message. The aha here is to take each number in its corresponding language and index the number into itself. For example, "cetyre" is 4 in Russian, and indexing 4 into "cetyre" gives the letter "Y". There are 12 languages total, with the country flags helping to confirm the languages used. The initial flavortext message then gives the following:

The message YAY KEEP GOING confirms that we have the correct mechanic and we can now apply it to each of the heptominos. To help with error correction, there are 24 unique letters among the pieces and each language contributes exactly 2 distinct letters. The mapping of letters and the translated pieces are shown below:

At this point, we need to use entanglement. The lightbulbs in the bottom diagram are so far unused and thematically irrelevant to this puzzle. They act as a clue to the entanglement. It turns out that the 17 heptominoes fit inside the Akari grid in Light Show so that each heptomino overlaps exactly one lightbulb. See the Light Show solution for how the heptominoes fit in.

If we look at the lightbulb on each heptomino, it turns out they are on the letters A through S and the heptominoes are presented in alphabetical order of the lightbulb letters. In Light Show there is also the leftover cluephrase ONLY USE BRICK IF ITS SEEN LIGHT FRSDHGLOIKEPBNMAJQC.

The next step is to look at each heptomino and only keep the bricks in that heptomino that the lightbulb in it shines on. The ending string FRSDHGLOIKEPBNMAJQC gives us an ordering on the 17 heptominoes and we can place the pared down shapes into the diagram at the bottom, using the lightbulbs and their corresponding rotation to place each piece. Here is what the diagram looks like with the pieces filled in:

Within each bordered box, the pieces form the shape of a number and the top border of the box lines up with a country flag on the left. Repeating the mechanic of indexing into the number in that language by itself, we get the final cluephrase: TWO IN ITALIAN. In Italian, the number two is the answer DUE.

Author's Notes

This puzzle went through a lot of iterations. It was primarily designed to support the cool grid structure in Light Show and initially just consisted of the heptominoes with letters on them and another logic puzzle involving fitting in the pared down heptominoes and then extracting letters. The initial testsolve feedback was that this puzzle really felt like the "abandoned brother" of the two, so I spent a long time trying to flesh out the puzzle.

At this point though, the entire Akari grid, heptomino shapes, and all the phrases in Light Show had been nailed down and it would have been a lot of work to change them. I could really only add to this puzzle by having a first step that resolved to the letters on the heptominoes or by trying to design a different extraction with the pared down heptomino shapes.

The idea to use languages came about as I tried to brainstorm ideas based on the answer DUE and learned that it was 2 in Italian. I thought about numbers in other languages and wondered if it'd be possible to do something uncoventional where a number indexes into itself. It was a challenge finding languages gave the 24 letters required for this pair of entangled puzzles since I wanted each language to contribute exactly 2 letters, in additional to contributing a letter in the initial phrase YAY KEEP GOING as well as a letter in the phrase TWO IN ITALIAN. I'm fairly happy with the final list of languages since nearly all of them are major languages.

The final extraction where the pared down heptominoes formed numbers was also very difficult to construct. I had originally hoped to construct each number separately without any overlaps, but decided that there simply weren't enough pieces to use, after trying for a bit. I was almost ready to give up on this extraction and use something simpler when I realized that it might just work if I allow numbers to overlap. This still took quite a bit of construction work, especially since the order of the pieces was partially constrained by some of the lightbulb letters, but I was able to make it work in the end and have all the numbers be readable.