As far as I know, Command Prompt, Powershell, WSL, etc all use the same underlying font system, TTF. And not many fonts have a TTF version. If you try using an OTF it won't be detected.
On machines that predate the new ConPTY replacement mechanism (so, everything before Win11), any app that is a command line program (such as cmd.exe, Powershell, anything compiled to be a console program and not a GUI program (this can be any program, and is chosen at compile time)), it is ConPTY.
ConPTY can see OTF fonts (afaik, I remember that working, I don't have a system old enough to check), but can't see any fonts that are in your user font directory (%LOCALAPPDATA%\Microsoft\Windows\Fonts).
As of Win11, however, ConPTY (which has been in existence since NT4, and has been an ugly pain in the ass for just as long) has been replaced with a mechanism to allow you to chose which one you want: a user supplied terminal that can supply that dependency (currently only Microsoft Terminal, but it is documented so any terminal can do it), or a ConPTY replacement owned by the Terminal team (which is basically the renderer and parser ripped out of Terminal, and a massive in-place upgrade, while still looking and acting like ConPTY otherwise). If the old ConPTY can't see OTF fonts (which would stem from using the oldest and most classic font API still in Windows), the new one can (as it uses DirectWrite).
On Win11 machines set to use Terminal instead of new-ConPTY, launching cmd.exe, Powershell, WSL.exe, or any other console program, will launch Terminal to display itself if not already in a console session.
However, fundamentally, for the entire conversation preceding this, it doesn't matter if a font is TTF or OTF for the purposes of supplying Unicode or Nerdfonts icons. OTF only matters if you want Type1-style glyphs (cubic Bézier curves vs quadratic) or want to use OTF features (which aren't meaningful for terminals, generally).
* Windows shells (at least for me, right now) won't DETECT a .otf font. You can't even choose to use it in the options of powershell/prompt/etc
* Most nerd fonts don't bother to convert to TTF. They only provide an OTF.
Even if they're fundamentally the same that doesn't matter if Windows won't detect it in the first place to let you select it.
This ConPTY replacement ('Windows Terminal') sounds fairly recent, so I think you'll forgive me if I didn't know about it. Our work machines only updated to Windows 11 in the last couple of days.
In any case, without access to the store I can't install it anyways. Nice for those who are on 11 already and have access though.
So, the issue with nerdfonts is the project, itself, is broken and flawed.
They use the nerdfont patcher, which mainly mutilates fonts, and often breaks them trying to add the nerdfont glyphs. The nerdfonts project also distributes these broken fonts while ignoring the font licenses, and also ignoring the fact that fonts update and then nerdfonts refuses to patch and distribute the new version.
Many projects distribute both OTF and TTF versions, while nerdfonts only distributes the patched OTF version (as you, indeed, have noticed).
The upside is, since the patcher exists, you can just run it on your own fonts and do whatever you want.
I highly recommend avoiding nerdfonts altogether, disable it in any program you find it in, and also consider filing bugs with those projects to entice them to remove support entirely.
Unicode exists for a reason, and fonts should strive to cover as much of it as possible. Corporate logos and custom icons should not be enshrined into any font, not even as something niche like nerdfonts, even if nerdfonts lives entirely in the Unicode private use area (PUA).
I always try to push projects to, if they choose to support nerdfonts, to default to off. It is confusing for new users to have to install a specific font (especially when they probably already have their chosen font, and possibly one that can't be nerdfont patched) to use a program.
LSD, in particular, can just either turn symbols off or just map them to commonly available Unicode symbols (a "well formed" terminal font covers most of, if not all, of the Box Drawing, Geo Shapes, Legacy Computing, and Arrows Unicode blocks, which is all you really need).
You could use Windows Terminal instead? Or does it have the same issue?