Playing by yourself is also a personality/developmental thing. I tried everything with DD. Timers, ignoring, a sticker chart....yeah no. Nothing worked. She just hated to be by herself and all attempts to make her entertain herself failed miserably.
She’s 7 now and is perfectly capable of finding something to do on her own. She generally chooses playing soccer or drawing. She still prefers to be on the same floor as me though. She’d also choose playing a game or even helping me clean over playing by herself. I no longer feel like the entertainment staff though. It just takes time for some kids.