Building on the earlier suggestion, hes totally right about the sweat ruin. You gotta check the IP ratings... the 4 in IPX4 is what saves your gear from dying mid-burpee.

• Sony Float Run Off-Ear Wireless Headphones dont go in your ears, so no sweat buildup.
• Sony WI-C100 Wireless In-ear Headphones are cheap and have that IPX4 rating. Be careful with neckbands bouncing tho, secure them under your shirt.

Honestly, do not get the big over-ear headphones for HIIT. I tried using my old over-ears for box jumps once and tbh they flew off my head immediately, not to mention the sweat made the pads gross within a week. For high-intensity stuff, you definitely want earbuds with decent water resistance. For your $200 budget, the Sony LinkBuds S Wireless Noise Cancelling Earbuds are probably your best bet. They have an IPX4 water resistance rating, so sweat wont ruin them, and they are super light so they actually stay in your ears when you are jumping around. The noise cancelling is pretty solid for tuning out gym music too. If you want to spend a bit less and save some cash, look at the Sony WF-C700N Truly Wireless Earbuds. They go for around $100, have the same IPX4 rating, and are actually smaller than the LinkBuds, which makes them really secure. The sound profile is punchy, which is great for workout music. Let me know if you need any info on how the companion app works for tweaking the bass, I can easily walk you through it.