Palm incorporated a phone into their PDA just before the iPhone was released. Blackberry likewise. It's called 'convergent evolution' where two paths evolve towards a single solution. It's why both fish and whales have fins.

The only criterion you have specified that discounts about 98-99% of today's smartphones is "An important thing is that it should run neither Android nor iOS, so that there won't be a possibility of distractions like games."

That's easily fixed. You just delete the games.