Based on a hash of a binary subset of the file. See Properties > Proxy > Copy Hash Code. Then, it looks in a proper project folder or app data (or custom folder) for a folder named proxies with a file named based on the hash code.
I set the proxy storage folder to a subfolder named ‘proxies’ within my project folder.
That’s not necessarily the best way. A proper project folder is created using New Project > Start. If you created a proper project folder, all you should do is Settings > Proxy > Storage > Use Project Folder. Otherwise, if you start a new project without doing something special it will start generating proxies in your old project folder. The checkbox makes it track the project folder automatically. Your way does not.
A converted clip does not track its source; it is a new source. It has different bytes and a different hash code. It gets it own proxy. Basically for your workflow, you need to convert before making proxies. You can do that by turning off proxy initially to convert many. Then, turn on proxy. Upon doing so, it will prompt you to generate proxies for them. Admittedly, the combination of conversion and proxy is not great.
Or maybe you do not actually need to convert files and can simplify this.