For your upstairs tv 2.1 where you only have 2.1 setup, why bother buying an AV receiver or AV pre pro + power amp? Just get a good quality stereo integrated amp with HDMI inputs that can also do bass management. I’m sure you listen to quite a bit of music too in this room.
The Classe Sigma 2200i stereo integrated amp has HDMI inputs and bass management and a subwoofer out. It supports 4k pass through. It has manual PEQ. It sounded really good and has tons of power. But the Classe Sigma 2200i will digitize its analog audio inputs. This is a direct digital amplifier. For your music sources I would highly recommend using its USB DAC input, and for your video or AV sources just use HDMI inputs.
I'm assuming you have some AV or video sources in this TV room otherwise there's no point of having a TV.