It is interesting to observe that not all the interior arrangements are provided for by developers (many are are optional subject to individual taste and preference) in Japan.
Only the basic items such as wall finishing, lighting, kitchen/bath room utilities are usually arranged as standard equipment.

Luxury homes the developer sells with interior fit-out and air conditioning provided.

'Fit-out' is more often used in a commercial context as in 'store fit-out' but in Australia is also used in a residential real-esate context.

Japanese term (edited): ���A���Ǝ�

I suppose your understanding is basically correct as to "interior furnishing" which is more characterized of its installment of architectural finishings rather than decoration which is more often referred as "interior" in Japanese. However, the business who does this job would be the one who designs all those installments, therefore probably they would be naturally called "interior desgin company (office, agency and so forth)".

Saying above, I still regard the word "interior decorating (decoration)" may not be deviated from the definition of the term used in the Japanese context. Perhaps both designing and decorating aspects may be involved in all the expected procedures for this interior coordination. Never know.

HIH

Japanese term (edited): ���A���Ǝ�

I don't list any web references, but I just spent a week in India dealing with a host of interior fitters responsible for the fit-out of an office we are building near Delhi.

In this context, 内装　refers to whether the unit is sold as a shell or with the interior work also done. It refers not to decorating or upholstery, furniture, etc. but whether the interior walls, flooring, electrical, and even plumbing and air conditioning work are done first or not.

The actual 業者 handling this work is a handful of contractors with thir own specialties - handling thigns such as gypsum wallboard, false walls (non-load bearing walls), electrical, flooring, wall covering (paint or wallpaper), ceiling, built-in lighting, window and doors, etc.

Your context would be translated as: (units are) sold with finished interiors and air conditioning. 内装 is wide ranging so it is just translated as 'interior'or 'interior fit-out'.