Festool has applications US20220001570A1 and US20230278153A1 pending in the US but not issued. I do not know if they apply to the Domino but Festool does not seem secretive about patents.
They do have some issued US patents. US7290967B2Dust extractor device for a router. As one comment says, patents are for inventions not for products. It is possible that only one feature of a product is covered by something like a dust removal system that might not be key to the primary feature of the tool but still prevents a clone of it.
A web page for a Domino model does say -
Patented routing principle
The spiral cutter rotates and oscillates to create perfect mortises.
If this is untrue and found to be the equivalent of patent mis-marking, it can get them in trouble but doesn't help you. Maybe they are referring the the rumored German patent.
Issued patents are publicly available and a company considering producing a new product can have a freedom to operate search done. This compares your planned product to all relevant patents and it does not require any information from the company you are trying to knock off.
If a patent covers your planned product you can try to find the owner and negotiate a license or you can change your plans or just take a chance and go forward.
Companies are not required to inform the public of the patents they hold which they think cover aspects of a product. One can find patents held by a particular company but it is not possible to always know about patents a company bought from another company or an inventor. The USPTO provides a way to record transfers of ownership but there is no requirement to use the recording facility.
Companies do have an incentive to mark products with the patents that apply. They can get back royalties in an infringement suit since a copier was on notice. However, patent infringement can be done even if you are unaware of a patent and even if you independently made the same invention.
they do not need to tell you what patents they have that cover one of their products but they do get a benefit from proper patent marking and mis-marking is not allowed.
They do not need to inform you before suing but usually do.
there is no “excuse” for patent infringement. Them not answering a question about their patents does not help you. However note that willful infringement can be penalized by tripling the damages.