Yea, addr:housename is usually the name of a single house but I do not see any reason why it should not be used for a “Hof” consisting of a couple of house units. I did not consider addr:block as this is meant for a city block acc. to the wiki. Nevertheless addr:block as well as addr:housename could be useful in your case imho.
According to ALKIS there is no address or housenumber like “Eisenberg 1” in the compound and the area is labeled as “Feriendorf Hannover” (which is not an address anyhow).
That is why I understand that Eisenberg 1 is not part of the official address but just used by the administration of the Feriendorf. The postal address according to Deutsche Post is
Feriendorf Eisenberg
36275 Kirchheim
and I am sure every supplier of anything will surely find the place using this address.
The only road leading to the Feriendorf is the Eisenbergstraße and that is why I used it in the address tags - can be removed if not wanted. addr:place will do fine instead of addr:street:
addr:city=Kirchheim
addr:postcode=36275
addr:place=Feriendorf Eisenberg
addr:housename or addr:block=Fichtenhof
addr:unit=1 (2,3,4,5)
Would that suit you? From my point of view (looking for a scheme applicable for all kinds of holiday villages) it is still fine.
The whole area of the Feriendorf should have a “tourism” tag in my opinion as it includes all kinds of amenities/naturals/leisure being available for the use of the kids having their holidays there. There is no reason why parts of the compound should not get additional tags (for the swimming pond, playgrounds, pitches, grassy or wooded areas and the like) but all this is part of the Feriendorf. Compare it to the area of a school or kindergarten which is handled in the same way.
leisure=resort does not fit as it primarily features the “leisure” (every day free time activities) and not the “tourism” (travelling somewhere for holidays) aspect.
leisure=summer_camp does not fit as well as you mentioned already.
landuse=recreation_ground would be fine if the main purpose would be offering a recreation area open to the public but this seems not to be the case. According to the official website the main purpose is holidays for kids groups, school classes and the like.
tourism=holiday_village would suit best - used 48 times so far but not documented in the wiki -
this would be my persoal choice but I have zero experience in adding it to the tourism wiki page.
Btw: I do not see any reason to tag this compound as a MP. According to the KISS rule a simple polygon would do well.
Again I do not see any reason for 2 names “Feriendorf Eisenberg” and “Feriendorf am Eisenberg”. The latter has no significant difference to the first and I could not find it in any publication. Wherever you find information about it the name is Feriendorf Eisenberg “Günter Richta” and this is the official name as well.