The homology of $M_{0,n}$ is an operad in a natural way that is compatible with AG structure (like weights)  . The construction uses the operad structure on the compactification plus Gysin maps-- it is general enough that one would expect it to work in the stable $\mathbb A^1$ homotopy category. In fact, there you can likely define it as the Koszul dual operad to the homology of the compactification. I'm not well-informed enough to know whether/where this has been done, or whether the construction should work unstably as well.

The same goes for the Fulton Macpherson compactification of configuration space in affine space which is closer to the $E_d$ operad.

The homology of $M_{0,n}$ is an operad in a natural way that is compatible with AG structure (like weights). The construction uses the operad structure on the compactification plus Gysin maps-- it is general enough that one would expect it to work in the stable $\mathbb A^1$ homotopy category. In fact, there you can likely define it as the Koszul dual operad to the homology of the compactification. I'm not well-informed enough to know whether/where this has been done, or whether the construction should work unstably as well.

The same goes for the Fulton Macpherson compactification of configuration space in affine space which is closer to the $E_d$ operad.

The homology of $M_{0,n}$ is an operad in a natural way that is compatible with AG structure (like weights) . The construction uses the operad structure on the compactification plus Gysin maps-- it is general enough that one would expect it to work in the stable $\mathbb A^1$ homotopy category. In fact, there you can likely define it as the Koszul dual operad to the homology of the compactification. I'm not knowledgeable enough to know whether this has been done, or whether the construction should work unstably as well.

The same goes for the Fulton Macpherson compactification of configuration space in affine space which is closer to the $E_d$ operad.

The homology of $M_{0,n}$ is an operad in a natural way that is compatible with AG structure (like weights) . The construction uses the operad structure on the compactification plus Gysin maps-- it is general enough that one would expect it to work in the stable $\mathbb A^1$ homotopy category. In fact, there you can likely define it as the Koszul dual operad to the homology of the compactification. I'm not well-informed enough to know whether/where this has been done, or whether the construction should work unstably as well.

The same goes for the Fulton Macpherson compactification of configuration space in affine space which is closer to the $E_d$ operad.