Is ~.local/bin in your PATH?

I'll assume you're new to Debian, so apologies if this is not true. The reason I say this is because generally speaking, "installing with wget" isn't how one is supposed to install software in Debian, using a program called apt is. yt-dlp is available in Debian 13's repositories. What I suggest doing is running apt install yt-dlp as root. That way the app will be installed globally, meaning it'll work without the system spitting out the error you've described. And on another positive note, the app will get updated automatically whenever you upgrade the system.

If this isn't for you, suggestions from other users here are valid and helpful.

Did you make it executable?
chmod a+rx ~/.local/bin/yt-dlp # Make executable

What is the output of your $PATH? (feel free to anonymise usernames)
echo $PATH

I believe you simply downloaded the file to ~/.local/bin/yt-dlp, you did not install it. You need to either add that location to your path or you need to cd to that folder in terminal, then run the command. It will check things in the current folder when trying to run executables.

um, isn't it easier to just:
sudo apt install yt-dlp
yt-dlp -U

Add

PATH="${PATH}:~/.local/bin"

To your .zhrc or .bashrc (whatever you use) and either source the file or open a new terminal. Should be as simple as that (assuming +x permissions)

Have you consulted the 'README' that is both in the yt-dlp directory as well as the github regarding installation?

I found pipx the easiest way to install and manage a current ytdlp installation

sudo apt install pipx
pipx ensurepath

pipx install yt-dlp

Yes I know, it's an additional package manager, but it actually is a package manager and will therefore ensure the setup is correct

Don't Python scripts need python at the beginning of the command that summons them?

Alternatively, you can make an alias to ~/.bashrc: alias yt-dl="python3 /path/to/yt-dlp [options] " And replace [options] for flags you may want to always use, if any. Or delete if you just want the raw script to be tied to a terminal command.

Then reload .bashrc by running either source .bashrc or . .bashrc