If you are having problems with different radar modules, shelve them, and order the same as mine - which I know work, so will eliminate a big variable and question mark. You may be loath to abandon your original investment, but at less than a quid each and free postage the new ones are not going to break the bank.
I have only tinkered with my radar sensors in a haphazard evaluation manner, sometimes even sticking the radar sensor directly to the wemos device using duct tape! If it works for me in that situation, your lab environment should be a doddle for it.
I've always supplied 5v to the sensor from the esp modules usb 5v, so perhaps avoid adding external bench PSU clutter and associated wiring for the moment. Try to reliably reproduce my minimal setup, then fine-tune it from there. Ever since mmiscool mentioning that the esp pins are 5v tolerant I haven't bothered level-matching the input, and never had any problem because of it.
I've always tested the radar modules using the mobile phone connected directly to the esp device in AP mode, so no router or network. But I have a router within 1m of my desk, and have never been aware of any problems caused to anything when running the radar sensors on the desktop, sometimes overnight.
So bypass your router initially - run the esp device in AP mode and connect to it directly from your mobile... which will make problems with router disconnection irrelevent. You can still monitor your router connection via another device (eg: computer) to see if your router is still disconnecting when using the sensor. If so, then the problem is a temperamental router, rather than the radar sensors.
Hopefully one or more of those suggestions will resolve your problem, so please let us know what eventually does the trick.