Performance page is not staying alive as intended

Sometimes the performance page does a full reload when switching between tabs and sometimes it does not. Reloading the page makes the use lose their debugging state.

https://github.com/flutter/devtools/assets/43759233/ebf1a063-7613-4ac2-b7e7-768b9ff22a98

首先重现 issue 中描述的标签页切换行为，并将其与附带的录制进行比较。跟踪完整重新加载期间丢失了哪个性能页面状态；当切换标签页始终能够保留调试状态，且不会导致页面意外重新加载时，即视为完成。

由索引模型根据 Issue 内容生成。