Not for PS5 or a new PSP/Vita. Kids device in Japan https://www.tweaktown.com/news/68903/ps5-cartridges-real-patents-sony-kids-toys/index.html

Considering most of the money comes from SW purchase and that old SW don't sell as good it would be interesting to see if Sony could make a profit just launching PS4 portable together with PS5.

Thats a good point. A PS4p would obviously only work with digital sw (beneficial for Sony) and could keep users engaged (paying) through PS+ or PS Now subs aswell as widen their (already great) reach quite a bit, but they might still need to sell such a device at a reasonable profit, which could harm sales - then again the investment to make it happen is probably much lower than a real seperate handheld launch, so I think it might very well be worth the risk.

Yes I think it is worth the risk and probably would outsell PSVita for a fraction of the R&D and even manufacturing cost.

But besides PS+ (would people play as much multiplayer in portable as they do on the console? Perhaps, many smartphone games that are competitive have a good number of players) I'm curious on how many SW they would sell of the legacy SW (at least today almost 100% of the games are available digital, but size is massive for a portable) and if the attach ratio having only "outdated" game would be high.