it is slightly more nuanced, if you do static linking it is considered derivative work and does requires you to open it. Since the app is based on ffmpeg which is GPL(core is LGPL) i am curious to know how it is getting used.
Static linking of LGPL content (thus making it derivative work) only requires that it must allow "modification of the work for the customer's own use and reverse engineering for debugging such modifications".
Making your own code public is not the only way to achieve this.
You can also make available to customer object files and build instructions to recreate your software with the (modified) statically linked LGPL content. (if it's LGPL > 2.1 you have extra requirements: you need to provide all toolchains/dependencies and it must be actually possible to install a modified version on the hardware)
Granted, this is not commonly used but I've used this on some projects where dynamic linking was not available/desired by client.
i didn't bundle the ffmpeg in the app. It uses homebrew to install ffmpeg on the user's device. this is the acceptable way since ffmpeg confirms it on twitter/X.