Standalone Profiler records Play mode data while Editor is in Edit mode

Steps to reproduce:
1. Create a new project
2. Open Standalone Profiler (Windows -> Analysis -> Profiler (Standalone Process))
3. Change profiling mode to Edit Mode (notice that data starts coming in)
4. Change profiling mode back to Play mode (notice data stopped)
5. Disable and enable recording
6. If the data is not being recorded, click on the Editor to focus it

Expected results: Data is not being recorded as the Editor is still in Edit mode
Actual result: Profiler records Play mode data while editor is in Edit mode

Reproducible with: 2020.1.0a21, 2021.2.10f1, 2022.1.0b8, 2022.2.0a5
Cannot test with:

• 2020.3.29f1 (Upon switching to profile Edit mode on Standalone Profiler, Editor throws a bunch of "Sending message header failed" warnings and disconnects from Standalone Profiler)
• 2019.4.36f1, 2020.1.0a20 (Standalone Profiler was not yet introduced)