I think it is simply that she is waking up at the end of one sleep cycle. It is common for babies to wake up (actually adults do too!) at the end of each sleep cycle.
You can try to encourage her to go back to sleep rather than to play after the end of the first cycle. Try doing things that you have been doing (e.g., feeding, rocking, holding). Sing or talk softly to calm and soothe her back to sleep may help too. You can also try having someone else (daddy perhaps?) to put baby back to bed. Usually babies are just looking for comfort and would slowly learn to soothe themselves back to sleep as they develop.
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