How do I get Sonic Mania's true ending?

Since this question is still open, I'll expand our comments into an answer.

You have to be playing as Sonic to get the "good" ending.

This might make sense, as the link in your question says that:

the "good" ending is actually a lead-in to Sonic Forces, which features "classic" Sonic alongside the more modern 3D version.

This theory is echoed in the following links:

• Well, THAT ending!!!! Spoilers...

• (Huge Sonic Mania Spoilers) The implications of Sonic Mania's Ending

• THEORY: Is Sonic Mania's True Ending...

• So... About that true ending... (spoilers!)

Also note that you can get the "good" ending when playing as Sonic and Tails or as Sonic with & Knuckles mode enabled as well.