In general, the paper white in a proof is precisely defined in the proof standard and is also measured in every test report.
For PSOUncoated it is 95.00 / 0.00 / -2.00 in CIELAB and for PSOUncoatedV3 it is 93.50 / 2.50 / -10.00, i.e. slightly darker (93.50 instead of 95.00 for brightness L) and significantly bluer (-10.00 instead of -2.00 on the B axis, i.e. the blue-yellow axis in the blue direction).
Recycling papers differ not only greatly from type to type in the area of paper white, but even from batch to batch. So if a printing company orders the same recycling paper in January and in February, the paper mill may well deliver a slightly different white value of the paper, as the paper white of course depends strongly on the recycled paper qualities used for production.
A colour-binding proof for recycling paper is therefore not possible, as no standard has ever been worked out due to the different paper qualities and white tones.
It is recommended for the proof to choose a classic proof standard such as PSOUncoated / Fogra 47, which shows a rather neutral, unbrightened paper white in the proof. Place one side of the recycled paper next to the proof and mentally transfer the colour of the proof to the white tone of your recycled paper. This way you can imagine the later printing result quite well.