
Wooting
80HE
Elite gaming performance, deep customization, but divisive typing feel.

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I am using the k3 max, it is a great keyboard imo and fine for gaming, one of the finest keyboard I have used. Though it is more expensive than your budget. There is the Aula F75 pro which falls in your budget but it is not a low profile keyboard. I have no idea how it sounds as Ive never used it myself.
I will avoid the Razer, Corsair and Logitech G Pro. For me, G515 rapid is the only Logitech product worth considering if you really want something with HE + low profile + TKL. Of course there are better overall package out there, but this package is unique. For other options outside Logitech, Keychron K8 HE, K3HE, K2HE and J2HE are good options, Keychron offers very good web-based software . They are also hot-swappable means that you can replace the switches when they are not working probably after period of use. Wooting will not be my first choice if you are going to have only one keyboard, as it needs more modding to provide better typing experience and modding is another rabbit hole. Keychron is the overall more balanced choice.
keychron k3 or k7 might work good for your budget, they have bluetooth and pretty solid for gaming. i use k3 for work stuff and some casual games and battery lasts forever the dual connectivity is nice when you want to switch between devices quickly. works great with ipad too, just remember to check if you want low profile or regular keys before buying
For a 75% gaming keyboard, the Keychron K3 Max works pretty well, especially with the wireless feature and good build. The NuPhy Node series is also worth a look if you want something small and easy to clean Check out reviews about battery life and upkeep since that's important. people usually mention keyboardyeti for comparisons, so hit that up for more info on features and prices.
I went all out earlier in the year and tried a bunch of low profile keyboards. Nuphy air75 he / Keychron K3 / Nuphy air75 v2 / Keychron B1 / Logitech MX mechanical / Logitech MX / If you want to buy a keyboard that will last you the next 5+ I would spend the $$ on the Nuphy HE or the Kechron K3, specially if you are going to use it for gaming. Otherwise the best cheap is the Keychron B1. I kept the Nuphy He, because I loved the magnetic keys, and the Keychron B1 because I can take it anywhere. My advice is that if you are going to be moving around with any of these, you must buy a keyboard case. Non of them felt like they would withstand a drop. Note: I did not try the lofee because it was the only one that required me to pay shipping fees if I returned it, so I didn’t take my chance. But I have seen great reviews.
I was an original Kickstarter supporter for the Keychron K3 and enjoyed it for couple years, but I recently switched to the Logitech G515 TKL. Honestly, it’s day and night. Comparing the two, the Logitech wins on several fronts - switching between devices (Lightspeed vs. Bluetooth) is nearly instantaneous, whereas the Keychron (I had version with Bluetooth only) takes 2–3 seconds. The wake-up time is also much better. The Logitech is ready the millisecond you touch it, while the Keychron always felt a bit sluggish to 'wake up.' Even though both have brown switches, the typing experience on the Logitech feels superior, and the PBT keycaps are a major step up in quality. The only real edge the Keychron has is its portability—it’s still the better choice for travel. That said, my experience is based on one of Keychron’s earliest models, so they may have addressed these issues in their newer versions.

Wooting
80HE
Elite gaming performance, deep customization, but divisive typing feel.

AULA
F75
Budget king for thocky sound, but layout and software flawed.

AULA
F75 Max
F75 value with screen, but wireless and key layout issues.

AULA
F99 Pro Mechanical Gaming Keyboard
Value full-size with numpad, great typing, but poor software.

Keychron
K2 HE Wireless Magnetic Switch Custom Keyboard
Affordable HE with premium feel, but limited switch options.

Ranked #1
Wooting - 80HE

Ranked #1
NuPhy - Air60 HE Magnetic Switch Gaming Keyboard

Ranked #1
Logitech - G19 Programmable Gaming Keyboard with Color Display

Ranked #1
Keychron - K10 Version 2 Full Size 104 Keys Bluetooth Wireless Mechanical Gaming Keyboard