Wow this is wierd, I managed to reproduce the bug in the released webgl version but not in the unity one. I will try to patch it after the jam! Still thanks!
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If I had to guess, are you perhaps using coroutines or awaitables to handle the delay between movements? If so, that might be the culprit. I recently encountered a similar problem where the bug only happened in a webgl build. After searching for the cause, I found that courotine WaitForSecond and Awaitable WaitForSecondAsync can behave inconsistently in webgl.