1. Where is the bookmarking feature? The star next to the score doesn't seem to do anything. If it's an icon to indicate score, it would be clearer to use a different icon.

2. For consistency, I'd use text headings at the top left of the time and score boxes, or at the very least put the icons on the left.

3. The 'View Solution' animation playback is confusingly fast. I'd add a step-by-step playback with forward/backward buttons as the default mode. You could still offer a checkbox to enable auto-playback, and a slider to adjust playback speed.

4. Since this seems to be based on the same toolkit Lichess uses, using the same color behavior for moves would be helpful.

5. Please offer a checkbox to enable showing possible moves when pieces are clicked like Lichess does.

I like the concept! But I believe to make it work better, the repetition should not just of the same puzzle but of the same theme/patter (last rank attack, fork, overloading etc…). Yes, the strict time constraint seems to work for me, but 15 seconds is too short for me to verify any idea, thus I could only react instinctively, which is quite bad in chess.

There are some bugs in the program, for example you said on loop 6, the time should be 30 s, but it was only 15 and the loop count was still 1. And it definitely needs a saving/synching feature because even now, one will lose his status just by refreshing the browser.