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.

On my personal computer, ~/bin has two directories within it.

One is for my .sh files and the other contains system links to them. The system link drops off the .sh and all scripts are added to my PATH

Just put the shebang at the top of your script:

#! /usr/bin/env bash

I’m not a big fan of extensions because if you put the script in your $PATH it’s weird to type do_the_thing.bash