Is there a disc burning program with a dark mode?
Yes. Burn by Zaweba has Same as Windows, Dark and Light themes in Settings, so the disc burner can match a dark Windows desktop.

One that does is Burn by Zaweba. It has three themes in its Settings: Same as Windows, Dark and Light. Choose Dark for a dark window all the time, or Same as Windows to follow whatever your Windows desktop is set to. It's free, offline software for burning CDs, DVDs and Blu-rays and working with disc images.
Many older burning programs were designed long before dark mode existed and still show bright white windows. On a dark desktop, late in the evening, that's a glare you notice.
Choosing a theme
Open Settings with Ctrl+, or from the menus. The theme is the first choice there. Same as Windows is a sensible default, because Burn then changes with the rest of your desktop if you switch Windows between light and dark. Pick Dark or Light if you want Burn to stay one way regardless.
Settings also holds the check after burning, the finish sound, Advanced mode and the Explorer right-click commands, and shows where Burn keeps your settings, backup sets and backup log, in %APPDATA%\Zaweba\Burn, with an Open button.
Why the theme matters for disc work
Disc jobs can be long. A multi-disc backup asks for each disc in turn, and copying a disc several times means feeding in blanks one after another. If you're doing that in the evening, a dark window beside your other dark programs is easier on the eyes. Burn also shows each job's progress on the taskbar button and the tray icon and plays a chime when it's done, so you don't have to keep the window in view at all.
Light suits a bright room or a shared screen, where dark text on a light background reads better. It's a matter of what's comfortable where you work.
Whichever you choose, the setting is saved with the rest of Burn's settings and applied the next time you open the program, so you set it once and forget about it. If you change Windows from light to dark later, Same as Windows means Burn follows without you visiting Settings again. The choice affects only how the window looks; every page, option and tool is the same in both themes, so nothing is hidden or moved when you switch.
Beyond the theme
A theme is a small thing, and it's not why most people pick a disc program. Burn's front door is the Backup Assistant, which plans, burns and checks backups across as many discs as needed. Alongside it are data discs with a live capacity bar, audio CDs from MP3, FLAC and other music files with CD-Text titles, saving your own audio CDs as files, and a full set of image tools to create, convert, mount and burn ISOs.
Keyboard users are looked after too. Ctrl+N starts a data disc, Ctrl+B opens the Backup Assistant, F5 looks for drives again and F1 opens Getting started, while Alt with a menu letter opens each menu. Help > Keyboard shortcuts lists them all.
Burn by Zaweba is free software for Windows 10 and 11, offline and with no account. Set the theme once and it remembers.