No. The DSi runs a closed proprietary OS. There is no App Store for third-party applications (unlike smartphones).
.nds homebrew from SD card. Emulators (NES, GB, GBA), media players, DSLinux. Requires technical steps; bricks possible if wrong.Low RAM (16MB), ARM9/ARM7 CPUs, no GPU—can't run modern apps (YouTube, Discord, browsers).
For apps, use a smartphone. For DSi, enjoy the games and Flipnote Studio.