Is "nuancedly" an existing word?

You're probably thinking of the general rule:

Adjective + '-ly' = Adverb

taking a noun modifier and converting it to an adjective or verb modifier. If X is the adjective, then 'X-ly' means 'in an X manner'.

Some examples are quick -> quickly, careful -> carefully.

But rules aren't perfect. 'fastly' is not a word, 'brownly' and 'sevenly' are not words.

Also, just because there is the possibility that a rule could apply, other forces can come in to play. In English (and in most languages), the sequence 'tl' is ... inopportune (hard to pronounce for adult speakers). Even if the adverb construction made semantic sense, the construction of adding '-ly' would still not be felicitous sounding and people would tend to avoid it.

There are exceptions to this exception, which are not really exceptions. For example 'forcedly' is a word, except that 'forced' (pronounced /forst/) when converted is pronounced /for.sed.liy/, creating an additional syllable which helps separate the 't/d' from the 'l'.

In general, taking a past participle as an adjective and trying to form an adverb out of it by appending '-ly' comes out sounding infelicitous (i.e. 'nuancedly' just ain't a word and probably won't catch on no matter how much you push it). So don't bother trying. You can easily and more fluidly get around this by saying 'in a nuanced manner'. As far as style is concerned, you don't want to use this pattern too much (more than once or twice in a document), but you probably wouldn't want to use the pattern 'uncommon ADJ+-ly' too often either.

Nuancedly is not a word. It has no entry in any English dictionary.

According to NGram Viewer, there is no trace of nuancedly in books neither.

The nuances of this theme are outlined in the novel perhaps?

I certainly wouldn't use nuancedly. While people might grasp what you are getting at, it's a bit clumsy and unclear.

It is a word, and several writers have used it (see e.g. the citations at https://en.wiktionary.org/wiki/nuancedly). But it's not common and not recorded in most dictionaries; many native speakers perhaps (for whatever reasons) consider it ungainly.