It never belonged to a servant (at least we are not told so). "Spare" means "empty" here, so "spare as a servant's" means that it was so empty it looked like a servant's room. (And now it's 'crammed' full...)

It's a special meaning of the word "spare." It's not too common and it's just a little bit literary or old-fashioned. Similarly, someone's body can be "spare," meaning thin or emaciated. Google finds me some examples of this usage. "Because there were two hundred guests, we had to decorate an assortment of rooms, some not normally used for parties. Some rooms had walls covered with beige-colored raw silk and left beautifully spare and unadorned, others were hung--actually cluttered--with portraits..." "His trumpet style, far from being likely to spearhead enthusiasm for New Orleans [jazz] music, was in reality a spare, stringent style, so plain and unadorned and undemonstrative that..." In "Nicholas Nickleby," I find that Dickens actually uses the word in several of its meanings: "Ralph fell back a couple of paces and surveyed him from head to foot. A spare, dark, withered man, of about his own age, with a stooping body, and a very sinister face rendered more ill-favoured by hollow and hungry cheeks..." [An actor makes] "spare and precarious earnings" "Meagre old chairs and tables, of spare and bony make, and hard and cold as misers' hearts..." "From out the most spare and hungry room in all this spare and hungry house there came, one morning, the tremulous tones of old Gride's voice..." ...and the more usual meaning of "extra" or 'unneeded" "paid the first week's hire in advance, out of a small fund raised by the conversion of some spare clothes into ready money..." "Mrs. Nickleby (having tea-spoons enough and to spare for all)"