Save variant triggers refresh in playground and loss of data

**Describe the bug**
When you click on save variant in the playground, you get a message, then the whole page refreshes and you lose all the information you had in the mean time

**To Reproduce**
See video

https://github.com/Agenta-AI/agenta/assets/4510758/33968464-7b8f-4a45-9f44-6a50f77c2c55


**Expected behavior**
There should be no refresh

