If we're talking specifically about executable scripts, here is #bash's (libera.chat) factoid on the matter:
Don't use extensions for your scripts. Scripts define new commands that you can run, and commands are generally not given extensions. Do you run ls.elf? Also: bash scripts are not sh scripts (so don't use .sh) and the extension will only cause dependencies headaches if the script gets rewritten in another language. See http://www.talisman.org/~erlkonig/documents/commandname-extensions-considered-harmful
It's for these reasons that I keep my executable scripts named without extensions (e.g. install).
I sometimes have non-executable scripts: they're chmod -x, they don't have a shebang, and they're explicitly made for source-ing (e.g. library functions). For these, I give them an extension depending on what shell I wrote them for (and thus, what shell you need to use to source them), e.g. library.bash or library.zsh.
Usually I have most of my (admittedly very few) scripts be .sh with #!/bin/bash. I do have a few that don't have an extension however, and those are in my $PATH intended to be used as shell commands
This is how I do it as well. Shell scripts that I include in a project are named with a .sh extension so other users can identify them easily. Scripts that I want to run as commands often are in my $HOME/bin/ and don’t have an extension. Sometimes those are convenience symlinks with easier names, so ~/bin/example might be a link to ~/repos/example-project/example-script-with-long-name.sh.
I stopped using extensions on anything meant to be an "executable" since it leaves me with the option to switch it's implementation. e.g. shell to python or some binary
I just drop it. Very little reason to use it when my ~/bin is nothing but shell script. If I made the script with the intention to share, .bash for bash specific script, .sh for POSIX compliant script.