As far as I remember you don't have privacy with Pheonix, one channel with their node means they at least see liquidity going in and out.
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On their privacy terms:
However, for convenience, your Phoenix application delegates the calculation of payment routes to the ACINQ node. In the current version of the wallet, this node will know the final recipient of the payment, and the amount sent. Work is being done to remove that limitation and have better privacy.
So no privacy.
When I say privacy I really mean regards to KYC. There are a lot of ways you can lose privacy even while running your own lightning node