Where do I put my computer purchase that was business expense on my return?

You will need to fill a T2125

In TurboTax Standard here is where you will access this information

1)  Go to the top tab called "INCOME" and answer yes to the first screen

2)  This will bring you to "Employment Expense Profile" select all box that apply's

3)  Fill all that apply's to your business expense and your computer purchase would fall under office expenses

Here is a link to tax tips on filing a T2125

Wouldn't a computer (or expensive peripheral) purchase go under depreciable assets (vs. office equipment)?

Yes, generally you would claim computers in the CCA section. But if the computer is inexpensive, like a Raspberry Pi, you can just expense it. 

Please note that the post you are responding to is from 2019 and may not be correct for the current tax year.