What is the D.A. Garden?

The D.A. Garden is a feature included in a few Sonic games as an extra. It's essentially an interactive sound test (like a visualizer). This name was first used for the Sound Test in Sonic CD, though I haven't seen any explanation for why it was named that.

From this article explaining the extras:

And the D.A. Garden – Also known as the Sound Test. This was what Sonic CD’s Sound Test was called.

Also, from the IGN Cheats and Secrets guide for Sonic Mania:

D.A. GARDEN

Here, Sonic Mania's soundtrack is available to listen to on demand.

It's called D.A. Garden because in Sonic CD, it was used to listen to the high-quality .cda audio on the disk, referred to as D.A. (Disk Audio). I'm not sure about Garden though.

Also, there is a separate sound test option in Sonic CD that is easier to unlock than D.A Garden, and is used to access a few hidden images and a secret 8th special stage by entering codes. In that sound test, you can listen to all sound effects and music (except intro and ending FMVs).