The competitor argument is interesting, because you could argue that Dreamcast was 5th generation by that metric. Yes, Sega was trying a war on two fronts. They wanted to outsell the PS1 and be prepared for a likely PS2.
Dreamcast hardware was discontinued globally before GameCube and Xbox hit the market, and only a year after PS2's Japanese launch.
Dreamcast spent the first half of its life competing against N64 and PS1, with the second half continuing that and adding PS2 into the mix.
Lifetime Sales Predictions
Switch: 156 million (was 73, then 96, then 113 million, then 125 million, then 144 million, then 151 million)
PS5: 115 million (was 105 million) Xbox Series S/X: 48 million (was 60 million, then 67 million, then 57 million)
PS4: 120 mil (was 100 then 130 million, then 122 million) Xbox One: 51 mil (was 50 then 55 mil)
3DS: 75.5 mil (was 73, then 77 million)
"Let go your earthly tether, enter the void, empty and become wind." - Guru Laghima
