About the video tools
A video file is a container holding a video track and an audio track, each compressed with its own codec. That distinction decides how long a conversion takes here. Moving a track from one container to another, MKV to MP4 with H.264 inside both, is a copy and finishes in seconds. Changing the codec, or compressing to hit a size limit, means decoding and re-encoding every frame, which is real work for your processor: a few minutes for a short clip, longer for 4K.
FFmpeg does that work, compiled to WebAssembly and downloaded once into your tab, which is why the first video tool you open takes a moment to start and the rest are instant. Nothing is uploaded, so a 2 GB recording never has to cross your connection; the limit is your device's memory rather than someone's upload cap.