Transport streams do not play on phones or in browsers and are awkward to edit. WebM is royalty-free and well suited to embedding in web pages. TS is at home in broadcast recordings and camcorder footage (MTS, M2TS); WebM is the usual choice for royalty-free video on websites.
The defaults suit most files. Under Options you can lower the resolution, trade quality against file size, remove the sound and trim the start and end. This is demanding work for a browser: a long or high-resolution file can take several minutes, and your device does all of it, so keep the tab open.
The conversion uses your browser's own video and audio codecs (WebCodecs), with hardware acceleration where the device has it; the file is read from disk as it goes and can be up to 2 GB. Where the browser lacks a codec, the page falls back to the compatibility engine. A video over 500 MB cannot be kept at full quality in browser memory; choosing a lower resolution or quality under Options lets it fit.