Is it safe to do a three-way splice in a single gang junction box?
box fill for 12 awg wire has a multiplier of 2.25.
the ground wire is only counted once so with 3 cables plus the feed 1x2.25 for the ground 8x 2.25 for the 4 hot and 4 neutral.
There is no switch or device in this box so we could skip that but if there was 4.5 adder would be needed because 2x of the largest wire connecting to it.
The integrated clamps in that type of box do not count but if internal clamps in the box that would be a 2.25 adder.
so right now with 9x 2.25 The required volume would be 20.25 cubic inches
The box you listed is a little undersized. When I have this many cables I usually go to a 4 square box they do make 4 square old work boxes but those usually require clamps and a 2 gang face plate because a mud ring (single gang adapter) kinda messes up the old work idea. A 4 square x 2-1/8 deep would provide 30.3 cu inch if you wanted to put the device in that box it would be large enough for that and the clamps.