So I'm no expert but I believe there are actually two different notions of hardware acceleration at play here:
1) HW accelerated rendering in Firefox, which despite being unfortunately disabled by default on linux can in my experience be enabled (on about:config) without issues. This makes the experience of scrolling much smoother, so I usually do that. I don't think this has any observable effect on battery life for me. However, enabling this in Sway results in some very odd behavior that breaks certain things so I've had to disable it. I can go into more detail on that if you like.
2) Hardware accelerated video decoding. In contrast to the fist one, this makes a HUGE difference in CPU usage and battery life. However this unfortunately cannot be used in any browser AT ALL in Linux, regardless of setup or configuration. The way I watch youtube videos on my laptop is usually with mpv, which does use hw decoding if it is configured to do so.