Things I learned while building a yt-dlp wrapper

This is a misunderstanding of the LGPL license requirements, as they are usually interpreted. LGPL requires that if your application dynamically links to a modified version of the library, then you must make the source code _for the modified version of the library_ open source.

The original use case for the LGPL license was the C runtime, which practically every binary on a system will link to, proprietary or otherwise. The idea is that the binary can be closed source, but any modifications made to the C runtime itself must be distributed. The idea is that an end user could take your modified version of the C library and further customize it to their needs.

In the context of bundled ffmpeg and ffprobe executables, the user could replace them with their own versions. You should make clear which version of the source was used to build them and if you have made any modifications, those must be open source.