Which insurance covers road damages caused by a crane parking area?

The crane for our timber frame prefabricated single-family house construction will partially be standing in the public space, in front of our property, on the street. If the public street is damaged as a result, who is then responsible for the damages? Is there an insurance we need to take out for this case, or is the crane company insured accordingly? (We already have various insurances, but as always I want to ask you first before contacting the insurance advisor. ;-) ) Or can/should the crane company lay steel mats or similar on the street to prevent damage?

Since our building area has been fully developed for about 15 years now, except for our property, there is no longer a construction road but only the regular publicly accessible road.

We were not allowed to do that at all, the regulatory office rejected our application because the applicant is liable for damages.
Therefore, the closure had to be applied for by a company. This company is then liable for any damages.
That’s why it was handled by the general contractor or the crane company in our case. The crane companies themselves have such insurance.