Removing halo effect in image composition: Google Meet's solution
Based on what I read in your reference I would say that
The key part for this solution is the model to compute the mask, if you have one that is a good starting point.
The second important feature is that it uses a position dependent filter, and the filter is parameterized with the length of the value of the mask. In their word avoiding the foreground to bleed in the foreground. They don't know how exactly, but I would say that from the mask a parameter $r_{i,j}$, that is large for the foreground and small for the background.
The possible realization of separable filter would be
$$ v_{i,j} = \frac{ \sum_k f(k\cdot r_{i,j}) x_{i-k,j}}{\sum_k f(k\cdot r_{i,j})} $$
$$ y_{i,j} = \frac{ \sum_k f(k\cdot r_{i,j}) v_{i,j-k}}{\sum_k f(k\cdot r_{i,j})} $$
And you are free to play with the normalization factors.
Using separable filter means that you use two 1D filters rather than small 2D filters for the image in multiple resolutions. This may be better in terms of memory. It can be implemented with two copies of the image, $x$ is written to $v$, and the second equation update the image $x_{i,j}$ in place.
Other possible advantage, since the filter is computed for every pixel separately. A separable filter of size $N \times M$, would require $N + M$ evaluations of the filter, while a 2D filter would require $M \times N$ evaluations, and in the realization above since the horizontal and vertical filters are the same it will require only $N$ evaluations.
Having the mask dependent filter is important to pass the foreground (the faces) with little distortion.