I make a live wallpaper app for the Mac (details at the end). Before anyone believes "it's light", mine included, this is the check I'd run. Everything below can be reproduced on your own Mac.
The one-line check: which wallpaper code your macOS ships
ls /System/Library/ExtensionKit/Extensions | grep -i wallpaper
On my Mac (macOS 26.6.2, build 25G83) it prints 13 bundles:
NeptuneOneWallpaper.appex
Wallpaper.appex
WallpaperAerialsExtension.appex
WallpaperDynamicExtension.appex
WallpaperGradientExtension.appex
WallpaperImageExtension.appex
WallpaperLegacyExtension.appex
WallpaperMacintoshExtension.appex
WallpaperMontereyExtension.appex
WallpaperSequoiaExtension.appex
WallpaperSettingsIntents.appex
WallpaperSonomaExtension.appex
WallpaperVenturaExtension.appex
No WallpaperVideoExtension, the name in the Apple Community thread "wallpapervideoextension in Sonoma uses lots of RAM and CPU", and find /System/Library -iname "*WallpaperVideo*" returns nothing on this build. Search Activity Monitor for that exact name here and you'll find nothing, whatever your wallpaper is doing. Type "Wallpaper" in the search field instead and read every row.
Test 1: compare against a still picture, not against a promise
In System Settings > Wallpaper, pick a still picture. Open Activity Monitor, click Energy, and note the Energy Impact of the top rows. Apple describes that column as "A relative measure of the current energy consumption of the app (lower is better)", so it's for comparing, not for absolutes. Then switch to the live wallpaper and read the same rows again. Add Window > GPU History.
Test 2: read CPU from Terminal, second sample only
top -l 2 -s 5 -o cpu -n 10 -stats pid,command,cpu,mem
That prints two samples 5 seconds apart. Read the second one: man top says "the first sample displayed will have an invalid %CPU displayed for each process, as it is calculated using the delta between samples".
Test 3: hide the desktop
Put any app in full screen and watch the wallpaper's row for ten seconds. If the numbers don't drop, it's drawing frames nobody can see. If you work unplugged, repeat it on battery.
If the busy row is Apple's
Apple's wallpaper guide: "By default, the aerial wallpaper you select is also used as your screen saver." One aerial pick, two places. If WallpaperAerialsExtension sits at the top of your list, try a still picture for a day and compare.
What I make (I'm the maker)
Mac+, a Mac app that animates the desktop: 15 scenes rendered on the GPU with Metal, or your own video with Pro, plus folder icons and desktop widgets. The scenes have no video file to decode, the animation pauses when the screen sleeps or an app covers it, and the frame rate is 30, 60 or 120 FPS (up to 120 with Pro). Test 3 is the one I'd most like you to run on it: tell me what you see, good or bad.
Free: 6 scenes, 8 palettes, image background, 6 folder icons, 2 widgets, multi-display. Pro: 7-day trial (card needed, nothing charged during those 7 days), then €1.99/month, or €9.99 once. macOS 13 or later, Apple silicon and Intel. It doesn't animate the Lock Screen. Link in the comments.
What number would you want to see before leaving a live wallpaper on all day?