My understanding is that 1) SR doesn't consider acceleration (it's an extension of Galilean/uniform motion), and that 2) when Einstein considered acceleration as well as gravity via the equivalence principle which lead to GR [1]. The key insight of the equivalence principle was that the force from gravity (e.g. standing on the Earth) is no different to the observer in their frame of reference to them being in a room in a rocket accelerating at the same rate as gravity [1], [2].

Thus, if you extend QED/QCD/SM in a similar way (thinking of QED/QCD/SM extensions in terms of acceleration and curved space with the equivalence principle in mind) that may lead to a quantized theory of gravity. -- Sir Roger Penrose has a similar idea/thinking [3].

One of the key challenges with quantizing gravity is in how the terms in the expressions resulting from analyzing the Feynman diagram interactions behave [4] which prevent them being renormalized. For electromagnetism you can formulate the terms using the fine structure constant (via the coulomb potential, ħ, and c) which results in successive terms decreasing in value and thus stabilizing to a single value.

For gravity using Newton's relationship between two masses in a similar way to deriving the fine structure constant you get Gm^2/ħc. Applying E=mc^2 gives GE^2/ħc^5. Using the Planck energy constant gives (E/E_p)^2 for the energy coupling strength. This means that unlike electromagnetism, the successive terms in the Feynman diagram analysis grows exponentially instead of decreasing to 0. Thus, this approach to quantization doesn't work for gravity.

Note: you can still use this to analyze quantum gravitational effects at small energies by evaluating to a given number of terms.

[1] https://www.britannica.com/story/how-albert-einstein-develop...

[2] https://www.ebsco.com/research-starters/physics/equivalence-...

[3] https://www.youtube.com/watch?v=VQM0OtxvZ-Y "We need to 'gravitise' quantum mechanics, not quantise gravity | Roger Penrose | Full interview"

[4] https://www.youtube.com/watch?v=yTEPm5d6mrI "Why Quantum Gravity Doesn't Work"

Can one really derive classical GR completely from a QFT of a spin-2 field? Or only a linear approximation?