I agree with your general idea, that perhaps life exists in non-chemical ways, but a galactic scale life form would be tricky for a ton of reasons - just one would be inter-organism communication.

The Milky Way is a pretty average galaxy and it's 100,000 light years in diameter. In humans, if inter-hemispheric signals takes 3ms you can achieve roughly 40hz "synchronic activity". Let's say (and this is a massive simplification) that the inverse of the maximum inter-brain delay is ten times the "clock speed" of the brain. That would give a human that lives 80 years over 100 billion clock cycles in a life, and a galactic brain that communicates at light speed (so 3e-13 hz "clock speed") only 9467 clock cycles in 1 billion years.

So one single human life would have ten million times more "clock cycles" than a billion years of this galactic life-form existing. Or, the galactic life form would have about 3 minutes and 55 seconds worth of "normal" human thought, from the moment it's born until one billion years later. I know human babies certainly don't do a lot in their first 3 minutes and 55 seconds.

Or, for a simpler example: say a massive star goes supernova at one end of the "brain", damaging it and requiring resources from the other side. It'll be a minimum of 200,000 years before that section gets repaired.