This Wiktionary entry seems to be saying that the English expression “The embarrassment of riches” (i.e., “[the problem with having] too much of a good thing”) is from a translation of (the title of) the 1726 French play “L’Embarras DES richesses”(one “s” in embarras and “DES” [richesses]).

According to this n-gram, “embarras DES richesses” was the version that was most prevalent through about 1917 (which could very well correspond with an important year in the life of the interesting subject of your biography).

However, again according to n-gram, none of the versions of the expression using “richesse/s” come/s close to the frequency of the nearly synonymous expression “embarras du choix.”

(cf: This French reddit thread also discusses this expression, with implications that the French “version” is actually used by speakers of English and that it’s perhaps not used at all in French-speaking countries.)

Peut-être voulait-elle dire:”Ce n’est vraiment pas pratique d’avoir trop d’affaires”. “Comment s’y retrouver au milieu de toutes ces choses / tous ce livres? / toute cette richesse?”

she said “ambara de riches“

is what you remember hearing.

So she was saying “(l’)embarras des richesses”. Most probably with the article : “L’embarras des richesses“. Not putting it makes it implied, and is really a spoken form.
There’s no reason to put an upper case for “Embarras” here. You will find it in a tittle (of a play, a book, a chapter) because the first term is an article, so the upper case also goes to the noun that follows.

Equally, L’embarras de la richesse (“The inconvenience from being too rich”) is quite an equivalent to it (“The inconvenience from having too much stuff / too much wealth”). You can use both forms alternatively. But since there was a play by that tittle, the first form – the one you remember – had some extra meaning in her mouth.

In that context, I would write it followed by a suspension mark or an exclamation mark, depending on her mood, tired or upset.

In such matter, the french idiom is (c’est) un problème de riches, what is sometimes translated by “(it’s) a first world problem”, expression used to minimize complaints about trivial issues by shaming the complainer, or as good-humored self-deprecation.