The answer to that is unequivocal: no. The underground observatory requires such stable and noise-free soil. This site would never have been considered if this border region had an increased risk of earthquakes and hence earthquake damage. Nor does the construction and subsequent use of the telescope at a depth of about 250 metres in the ground increase the risk of earthquakes. Compare it to a hard stone, into which a hole is drilled from one side to the other. That hole is very small in relation to the whole stone. That does not make that stone softer or more unstable. This is also how the construction of the Einstein Telescope should be seen in relation to the whole rock. Another comparison is with a car tunnel through a high mountain, e.g. the Gothard tunnel in Switzerland: the tunnel does not make the mountain unstable.
A comparison with earthquakes in Groningen due to gas extraction is also out of the question here. In Groningen, gas is under pressure in a porous layer deep below the surface. This layer owes its solidity to the presence of that gas. When you start extracting that gas, that porous layer becomes more unstable and that can lead to subsidence and earthquakes. That soil can become more unstable as a result, as has unfortunately been seen in Groningen.
Nor is there any comparison between the Einstein Telescope and mining in southern Limburg. In mining, entire layers were extracted from the soil, relatively close to the surface. This is comparable to gas extraction in Groningen: where the soil in Groningen has become weak or unstable by removing entire layers of gas, the same was the case in the South Limburg region by removing coal layers.