Added 4 minutes later
It turns out that the slowdowns disappear not only when listening to music but also when the Opera browser is running.
1. You downloaded H1TE and are playing without slowdowns - this means everything is fine.
2. If you experience slowdowns, play on H1TE_single_core.
For now, that's the approach.
The method of fixing the processor load in Heroes is not new. It is also used in other similar patches (inserting Sleep into the message loop). However, slowdowns are observed everywhere on XP. A partial solution may be to replace Sleep with WaitMessage: the slowdowns disappear, but there is "jerky" movement of the hero on the map while moving the mouse.