Does a unique Stripe price ID need to be created for each recurring donation level in the Donations app?

In short, no.

The Soapbox Engage Donations app can be integrated with Stripe to accept both one-time and recurring donations.  In the case of recurring donations, only one Stripe price ID needs to be created for use with a Donations app page, regardless of the number of recurring donation levels that are included on the page.

More information regarding configuring Soapbox Engage's Donations app with Stripe for recurring payments can be found in the following article:  Accepting recurring payments with Stripe in the Donations app.