Plenty of ergonomic chairs have a solid lounge option. Few are better at it than others. The LiberNovo Omni comes to mind, but I'm wary of the electronics. You didn't specify budget though so location & budget are needed to guide you anywhere. More on reddit.com

No ERGONOMIC chair is good for sleeping on, just avoid it. The way the seat and backrest/lumbar pieces are made are to support mostly an upright position, and literally falling asleep on a chair that has good support will put pressure on the wrong places inducing in numbness (nerve pressure) and bad circulation (blood vessel pressure). Not to mention most headrests are very lightly padded and made for upper nape resting as opposed to a pillow which would spread pressure along all of the nape down to the upper neck. This last one may cause the most stress, and that's even if you have a headrest because if you don't your head and spine will tilt backwards which is even worst. THAT SAID, there are some specialty lounge chairs that are somewhat ergonomical from the top brands such as the Leap lounge or whatever it's called. It's a 3k+ affair though and I have no idea if it's any good due to its rarity making it scares to find unbiased opinion online. I'm speaking from experience falling asleep myself in multiple decent chairs such as the Haworth Zody with a custom headrest, the Haworth Fern (custom pillow-sleeve at its top) and the Steelcases Please V2 (no headrest, but I can rest my head near its top). Horrible sleeping experience at any level, I wake up all aching after minutes of discomfort. The body just naturally rejects it. Great chairs for 30min-1h of recline playing games or watching media otherwise, but I still need to take a break or two in the longer movies. Also, even for short stint recline, you will absolutely want a footrest that's at least almost as tall as the seat height you're using. Any "racing/gaming" chair that will have a leg rest attachment will once again out pressure on all the wrong places of your calves. More on reddit.com

Have you considered adding something like this? I have an amazing chair thats rated for 24/7 use and is found in 911 call centers and government agencies and still use one of these. I only use the seat cushion part not the back but it makes sitting for prolonged sessions so much better. https://thecushionlab.com/collections/all/products/ergonomic-seat-cushion More on reddit.com

This is not what you want to hear, but you can't get a good chair for $100. $100 buys you a midrange chair at Staples whose padding will break down in the first year of use. It will probably break completely in a couple of years. The cheapest chair for "all the hours" you spend gaming is a used Aeron chair for ~$350 or so. You could also get any other used professional office chair, but Aerons are usually the cheapest. Such a chair will last you at least a decade, even used. I am currently sitting on one that I bought for $300 five years ago that was probably manufactured around 2000. All I've done to it is lubricated the hinges once. I fully expect to keep this chair for 15 years. That's $20 a year, and a great investment compared to the trash Staples chairs I have thrown away. More on reddit.com