Court wear is intrinsically weird. The dags on the bodice (waist) are characteristic of court dress, not normal clothes. "Garniture" is not a familiar term. Bodice would be a single piece. White skirt is second piece. Bustle & en train are a third piece. (Consulting with my professional historian girlfriend, who is also a Costume Society of America member).
Dressing up in a second bustle era may be helpful.
It is about 10-15 years later than the painting, but the only things that have changed are the shape of the garments. The bodice/skirt/overskirt (bustle) remains in essence the same.
I looked up the definition of garniture in the context of fashion, and I'm almost positive that it is not being used to describe the structure of the dress.
update
The gown may or may not be court wear, but it is quite formal as evidenced by the gloves and fan (indicating it's not for wear at home), the velvet (blue), satin (white, possibly taffeta but I read it as a heavier satin), and extensive gold trimming. The Russians were noted for exceptionally lavish clothing throughout the century, so perhaps this is "merely" formal.
However, from middle-class day dress to the highest couture and greatest formality, the basics of an era are the same - hence my reference to the video. You'd still be putting on a chemise and stockings, corset, bustle cage, petticoats, etc. It's just the exact cut and details that change. Think of it like how jeans and a shirt were very different looking in the 1980s than today, but in the fundamentals of how you wear them, and what is underneath, it's the same.
The structure and cut are extremely indicative of the early 1870s. Another feature of that decade - as with the decade prior and after - is front-fastening bodices. There is simply no need to bring in stomachers or other garments from centuries prior. Izabela Pitcher in her book gives a pattern in shape remarkably similar to this dress, but is actually taken from a 1873 gown in the Met collection. It has a center front button closure. Even Waugh, referenced by LangLangC, indicates in her patterns that front fastenings are typical. As do other references (two noted below, I doubt anyone really wants my entire library holding...). Likewise, there is no bertha. The lace around the top of the bodice is most likely trimming on the bodice. The white in the sleeve is the same satin as the skirt, indicating it is not a peek at an underlayer, but an integral part of the sleeve - much like the 16th century German Landsknechte was "faked" by stitching in fancy material to puff through the slashes.
So, then, to answer the actual question. In current American nomenclature, the outer garments would be a bodice (sleeves, front, etc. are all one piece), skirt, and trained (or en train) bustled overskirt. For all that they are very fancy, that's all they are - three pieces. The one bit I'm not entirely certain of is the white at the front neckline. That may be part of the bodice, or it may be a "modesty" infill as LangLangC suggested. Given the white down the center front, I'm inclined to think part of the bodice, but then this is a painting and subject to all the same artistic license as any other illustration. 1870s painting isn't like the Italian and Spanish Renaissance painters, who were often so detailed you can make out individual ravelled threads!
Beneath the dress would be, at a minimum, stockings, slippers, chemise, corset, overcorset, cage bustle, and petticoat. Not too dissimilar to those illustrated in the video.
Pitcher, Izabela. The Victorian Dressmaker. W&G Baird Book Printing and Prior Attire, 2018
Edwards, Lydia. How To Read A Dress: A Guide to Changing Fashion from the 16th to the 20th Century. Bloomsbury Academic, 2017