3 year old & independent play

Hey! Just wanted to ask other mums with 3 year olds how well they play alone? My child is literally like Velcro so we always struggle with playing alone. I’m a stay at home mum and we always try to do an activity in the morning or pop out to the park or somewhere else fun. We do lots of crafts, baking, messy play etc. but when it comes for any kind of play alone she just will not do it. Cries and says that “I never play with her and she doesn’t have anyone to play and can’t do it alone”. For context me and my husband probably spend TOO much time playing babies, Barbie’s, in her kitchen etc. maybe we’ve created a bit of a rod for our own back but we recently moved abroad and she’s an only child so think we’ve over compensated. Now she just wants the Tv on (which I won’t do) or she will just sit and throw tantrums because she doesn’t want to play by herself. I’m struggling to get anything done (by myself I mean as I often include her in chores!). She starts preschool in August and has the most fantastic imagination but just won’t play by herself for any amount of time. Any tips? Anyone else have a Velcro child? 😂 Feeling so much guilt because she should be able to play alone for small amounts of time!