Currently Online 
PSP was profitable but got clobbered by the mega-titan DS and even the aging Game Boy Advance was still competition before it was discontinued.
Vita was a failure, and pretty much DOA with the memory cards, price, and a shrinking handheld game console market.
A true PSP 3 (that is if you view PS Vita as PSP 2 which it pretty much is) is a big financial gamble for Sony. You have to build up a library of games between ports and native versions, an identity, proper pricing etc.
PlayStation Portal is a baffling product. Instead of that or a PSP 3, Sony should make a device similar to Steam Deck. PlayStation Now/Go/Remote or whatever you would call it with
1. Native PS4 library supported offline and online with or without streaming.
2. PS5 library supported when streamed from PS5
3. Bluetooth
4. Second screen functions with PS4 and PS5.
Lifetime Sales Predictions
Switch: 161 million (was 73 million, then 96 million, then 113 million, then 125 million, then 144 million, then 151 million, then 156 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
