Interesting… I hadn’t considered that this might enable linguistic “shorthands”, is that the implication?

Yes, it is! Agreement on its own already allows some "shorthands", if you're able to omit the nouns; but derivation in special allows a lot of them, because it allows you to cram more info into the word at the "cost" of 1~3 phonemes.

I'll give you some examples of that, using Portuguese for my own convenience; do note however you'll see similar stuff popping up in other gendered languages.

First example:

1a. O relógio (M) caiu sobre a mesa (F), e ele (M) quebrou.
1b. O relógio (M) caiu sobre a mesa (F), e ela (F) quebrou.

Both sentences mean "the clock fell over the table, and it broke", but the "ele" (he/it) in 1a refers to the clock, and the "ela" (she/it) in 1b to the table. By changing the gender of the pronoun, you can force it to refer to one or another noun, in a rather succinct way you wouldn't be able to do in a non-gendered language like English. (I feel like "it" would refer to the clock, as the agent of the first phrase, and if you want to refer to the table breaking you'd need to repeat the noun.)

Of course, this "shorthand" only works if both nouns happen to have different genders, but it's already enough to cram a bit more info per syllable. In other cases people use the same strategies as in English.

Second example:

2. Pedro tem dois gatos: uma (F) frajola (F or M) e um (M) malhado (M).

Translated directly, this sentence becomes "Peter has two cats: a tuxedo and a tabby". However the translation doesn't mention the tuxedo is a female, and the tabby a male. In a non-gendered language you'd need to either ditch those pieces of info or explicitly refer to them, and that takes more words.

I’d be interested in follow up studies to examine emergent linguistic patterns. Can we weigh syllabic encoding by common usage by age? If we eliminate “thouest” from the dictionary but include “skibidi” how does that skew patterns for informational density?

The impact for an individual word would be fairly minimal, I think. However, if you're systematically changing sounds or the grammar, like languages often do (cue to "want to", "going to", "trying to" → "wanna", "gonna", "tryna"), the impact will be fairly high. And likely compensated elsewhere, to keep the bits/second ratio roughly the same.

Science is so fucking cool and I’m stoked that people nerd out on shit that I’m an idiot about so I can learn about the nature of the world.

And the fun part is that everybody is an idiot for most topics, except a few individual expertises. We're basically a race of clueless apes trying to make sense of the world.