Welcome to the forum mps803,
My first thought is - are you sure you've got "eM Client" set as your Windows "Mail" default where you can choose your Windows default apps? (you might want to double-check to make sure your "Mail" default is in fact "eM Client").
That said (as far as taking the approach of entering a path in the POP Peeper "Email client" setting to your "eM Client" path location, instead of leaving the value blank), try simply doing a right-click on the "eM Client" desktop shortcut icon and select "Properties" to find the "exe" target location (TB example below) assuming the install placed a shortcut on the desktop -
if not read further down in this post for an alternate method to find the "target path" for the "exe" file:
then right-click copy the "Target" path and enter (paste) that "Target" path in POP Peeper (w/out the quotes) for the "Email client:" path setting (from the "Properties" window) to see if this works for you.
You mentioned quote: "My default email client currently is 'eM Client', installed from Microsoft Store (so there's no way of selecting path & EXE), but the same is true for Windows Mail included in Win10.". While you're correct to say there is probably an issue with "Windows Mail" because by design there is no .exe file extension for the app but rather an .mui extension is used (i.e. C:\Program Files (x86)\Windows Mail\en-US\WinMail.exe.mui), I don't see why there would be an issue with "eM Client" since it does use a standard "exe" file (see below).
In regards to the "eM Client" - you should be able locate the "MailClient.exe" executable that the "eM Client" uses which should be located in a subdirectory of "C:\Program Files".
If you don't have an "eM Client" desktop icon you can do the following (alternate method to get the executable path):
1) Look in your “Start” menu for your "eM Client" app and do a Right-click on the “Start” menu shortcut for the application.
2) Then select "More" > "Open file location".
3) This will open a File Explorer window that points to the actual application shortcut file. Right click on that shortcut to select “Properties”.
4) This will provide you with the "Target" path you can enter (copy/paste) into the POP Peeper "Email client:" path setting (w/out quotes).
Let us know if any of the above helped to resolve the POP Peeper Email Client issue.
Good judgment comes from experience and a lot of that comes from bad judgment. - Will Rogers