To best of my knowledge/understanding:
Yes, those extra fees (0.15% in, 0.25% out) go directly to the Spark Service Provider (SSP), even when you are using Cake Wallet's implementation.
Here is exactly why: When you use Cake Wallet's new "Lightning" setup, you aren't actually transacting directly on the Lightning Network. You are operating on the Spark statechain (integrated via the Breez SDK). Anytime you want to send or receive from an actual Lightning node, an SSP has to actively bridge the funds between the Spark statechain and the real Lightning Network. That 0.15% and 0.25% is the toll the SSP charges to act as that bridge.
To answer your second question: No, Cake Wallet does not charge an additional fee on top of this. Cake does not slap an extra premium on basic peer-to-peer sends. Their business model revolves around making money from their in-app token swaps, fiat on/off ramps, and Cake Pay services.
So while Cake isn't double-dipping on the transaction itself, you are still subjected to Spark's bridging fees just to interact with the broader ACTUAL/REAL Lightning Network—which definitely undercuts the "near-zero fee" ethos of running a real Lightning node.