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The Nintendo Switch Pro Controller should work, but LaunchBox itself does not handle controller input once a game is launched. LaunchBox hands the game off to RetroArch, so in-game button recognition is controlled by RetroArch and Android.
First, please confirm which RetroArch app LaunchBox is using for your Sega Genesis platform: RetroArch, RetroArch Plus, or a sideloaded RetroArch build. Each one has its own separate controller/config settings.
Try opening that exact RetroArch app directly, launch the same Genesis game manually, then go to:
Settings > Input > Port 1 Controls > Device Index
Make sure the Nintendo Pro Controller is selected for Port 1. Then check:
Settings > Input > RetroPad Binds > Port 1 Controls
and bind the buttons there. After that, save the RetroArch config and launch the game again from LaunchBox.
If the controller does not work in RetroArch directly either, then the issue is with Android/RetroArch seeing the controller, not LaunchBox. If it works directly in RetroArch but not when launched from LaunchBox, let us know which RetroArch version/package LaunchBox is set to use and which Genesis core you selected.

Hi!

Actually, yes. Playlists show all games added to them.

But when you enter a playlist, you can filter it by platforms.

Here is the list of the supported platforms:
 
3DO Interactive Multiplayer Amstrad CPC Amstrad GX4000 Apple II Apple IIGS Arcade Atari 2600 Atari 5200 Atari 7800 Atari 800 Atari Jaguar Atari Lynx Atari ST Capcom Play System Capcom Play System II Capcom Play System III ColecoVision Commodore 128 Commodore 64 Commodore Amiga Commodore Amiga CD32 Commodore PET Commodore Plus 4 Commodore VIC-20 Daphne Elektronika BK Fairchild Channel F GCE Vectrex Jupiter Ace Magnavox Odyssey 2 Mattel Intellivision Microsoft MSX Microsoft MSX2 Microsoft MSX2+ MS-DOS NEC PC-8801 NEC PC-9801 NEC PC-FX NEC TurboGrafx-16 NEC TurboGrafx-CD Nintendo 3DS Nintendo 64 Nintendo DS Nintendo Entertainment System Nintendo Famicom Disk System Nintendo Game & Watch Nintendo Game Boy Nintendo Game Boy Advance Nintendo Game Boy Color Nintendo GameCube Nintendo Pokemon Mini Nintendo Satellaview Nintendo Switch Nintendo Virtual Boy Nintendo Wii Nintendo Wii U PC Engine SuperGrafx Philips CD-i Sammy Atomiswave Sega 32X Sega CD Sega Dreamcast Sega Game Gear Sega Genesis Sega Master System Sega Naomi Sega Naomi 2 Sega Saturn Sega SG-1000 Sega Triforce Sharp X1 Sharp X68000 Sinclair ZX Spectrum Sinclair ZX-81 SNK Neo Geo AES SNK Neo Geo CD SNK Neo Geo MVS SNK Neo Geo Pocket SNK Neo Geo Pocket Color Sony Playstation Sony Playstation 2 Sony PSP Sony PSP Minis Super Nintendo Entertainment System TurboGrafx-16 TurboGrafx-CD Watara Supervision WonderSwan WonderSwan Color BBC Microcomputer System Emerson Arcadia 2001 Atari Jaguar CD Interton VC 4000 Mega Duck ScummVM Sega Pico Nintendo 64DD Philips Videopac+ PICO-8