Hiring SiGeKo for a single-family house?

Even for a single-family house, you must appoint a SiGeKo if there are workers from different companies on the construction site. This is clearly stated in the Baustellenverordnung. I have dealt extensively with this topic because we received an inquiry from the Bezirksregierung asking who our SiGeKo is. The SiGeKo can possibly also be done by your architect, provided they are willing and meet the necessary requirements, which is usually the case. Many do not want to admit this and say that it is not needed for small construction projects. The fact is that there is a law about it. Good information on the topic is available from the Architektenkammer NRW. Even though it is an NRW site, the BaustellV is a federal law, so it applies throughout Germany.

Thank you for the reference to the construction site ordinance.

It states that a SiGeKo is only necessary for construction sites with more than 20 employees simultaneously or a scope of more than 500 person-days.

That probably does not apply to a single-family house... in case of doubt, the client acts as the SiGeKo.

No, that is not correct. The 20 employees and 500 person-days refer solely to the pre-notification (see §2 (2)). This is repeatedly misread. §3 (1) is relevant. /Edit: see table under 2. in the RAB 31

From the description of construction services of Town & Country

Safety and Health Protection Coordination (SiGeKo)
The general occupational safety principles (§4 Occupational Safety Act) must be observed by the client during planning and execution - regardless of the size and type of the construction project. The client is responsible for ensuring that the general occupational safety principles are observed, that a prior notification is prepared and submitted to the competent occupational safety authority, that a safety and health protection coordinator is appointed, a safety and health protection plan is developed, and that documentation for later work is created. This was regulated as an implementation of the EU Construction Sites Directive in the Construction Site Ordinance to improve the safety and health protection of employees on the construction site and came into force on July 1, 1998. The contractor provides this service required by law free of charge and posts the alarm plan and the safety and health protection plan clearly visible on the construction site (back of the construction site sign).

Additional work for the client -.- with Town & Country

Description of construction services Helma: "...takes over all obligations within the framework of the Construction Protection Letter free of charge"

Theoretically you would need it, practically not. No one will ask for it either.

Additional work for the client -.- at Town & Country

Where is the additional work for the client? It says that the contractor (Town & Country) provides it.