Browser support is the whole story
This converter uses your browser's own image decoder. That is what makes it private — nothing is uploaded — and it is also its main limitation: if the browser cannot read HEIC, the tool cannot convert it.
Safari on iPhone, iPad and Mac decodes HEIC natively, so conversion works there. Chrome and Firefox on Windows and Linux generally do not, and the photo will simply fail to appear with no useful error. On Windows, installing the HEIF Image Extensions from the Microsoft Store helps some applications but does not give Chrome or Firefox the ability to decode HEIC in a canvas.
If you are on a device where this does not work, the most reliable route is to change what your iPhone produces in the first place — see below — or use a desktop application that has its own HEIC decoder.