It could be anything—gardening,cooking,music,sports—but whatever it is, make sure it's a relief from daily stress rather than another thing to worry about.

破折号的作用之一，是对前文某个词语的“列举、解释”，本句是对 anything 的列举说明，指个人爱好的具体内容。本句的两个破折号相当于括号：

It could be anything (gardening,cooking,music,sports) but whatever it is, make sure it's a relief from daily stress rather than another thing to worry about.

but 表示这两个分句并列（看红色）：

It could be anything—gardening,cooking,music,sports—  but  whatever it is, make sure it's a relief from daily stress rather than another thing to worry about.