Due to the release of Collection of Mana and the 3D Remake, I can't host any music files here. Rather, I can provide you with links to official services and other sites.
Trials of Mana (2020)
Square Enix has not officially added Trials of Mana's soundtrack to streaming services like they did for the original Super Nintendo version. I can only direct you to what fans have uploaded on YouTube.
Seiken Densetsu 3 (SNES)
Fortunately, Square Enix has made it easy for us to listen to the soundtrack for the Super Nintendo version of Trials of Mana/Seiken Densetsu 3. It's available on every popular music streaming platform.
The best place to listen to Trials of Mana/Seiken Densetsu 3 fan music is at OverClock ReMix. They offer hundreds of songs! They have also uploaded their music to YouTube. When you're looking for fan music, note that it would all be under Seiken Densetsu 3 (not Trials of Mana since that name is new).
Extracted Game Music
The fan base has gone a long way with emulation. In the early 2000s, they came up with 'extracted game music' (a.k.a. chiptunes). They extracted the programming of the music from every classic video game and built digital soundtracks with them. With special music players, you can play these music files as if they were MP3s. And they're far better quality than MP3 because it's the actual programming of the song that you're listening to! In this realm, Super Nintendo music is under the 'RSN' file format. Music players that support RSN can be found on any device: Windows, Android, iOS, Mac, and Linux.
My favorite feature about this music is how small it is. Seiken Densetsu 3's RSN soundtrack is around 300 KB while an MP3 soundtrack is around 400 MB! So you could quite literally have hundreds of classic gaming soundtracks on your iPhone or Android phone, and barely make a dent in your phone's storage.
If you want to learn more, read my tutorial for Extracted Game Music. My tutorial also provides links where you can download RSN music. Extracted game music can be converted to MP3, too. My tutorial provides directions on that process. Note that when you're looking for Trails of Mana's RSN soundtrack, you need to look for it under the Japanese name: Seiken Densetsu 3.
MIDI music is a relic from the early days of the Internet when it was the only music we could download with our slow dial-up connections. It's fan music because MIDI files are made by people playing the songs on electric keyboards. The #1 website for video game MIDI music still exists today: VGMusic.com. There you can download Seiken Densetsu 3's entire soundtrack in MIDI format.
Some official album covers and some custom ones.