What keyboard layout are you using? I can't reproduce on a US layout.
Javascript says the key I pressed was keycode 220 (same number as 0xDC) or key "\".
I had Tandy 1000 as the selected machine. When I look at the onscreen keyboard, I don't see a backslash key underneath backspace, but I do see one next to left shift. For keyboards that have the alternate backslash there, it is listed as having a scancode of 0x56 and a VKEY code of VK_OEM_102 (0xE2). (I haven't actually checked information specific to the actual Tandy keyboard)
I have to make all new pixel-art for a Tandy 1000 keyboard and PCjr keyboard. Fun
Backslash works fine if you have chosen to emulate the PC or PC XT. For PCJr, no keystroke appears at all (it does not act as backspace). For Tandy 1000, it acts as backspace. You get the same result whether you use the real backslash key or the backslash key from the on-screen keyboard.
The Tandy 1000 will need its own OSD since the tandy keyboard differs from the Model F in significant ways. You'll notice that if you type shift-backslash on the current model-F based OSD you'll get a 7 instead of the expected |. Because backslash is on numpad 7 on the Tandy.
Dealing with this stuff is tons of fun