I'm not certain exactly what you are looking for. There are a few ways which I can see interpreting what you're asking for. How to implement it, or what to use, is going to depend on what you want and what's comfortable for you.
Bookmarklet(s)
Your code currently replaces the content of the text area with the text you've put in the bookmarklet. Personally, if I were creating a bookmarklet for this, I'd probably look at the code in the answers to How to insert text into the textarea at the current cursor position?, which would instead insert the text at the current cursor position, rather than replacing the content.
You could implement additional features, such as taking the content from a URL. However, that rapidly goes beyond something which would normally be implemented as a bookmarklet and into what would probably be more appropriate as a userscript.
Userscript(s)
It's certainly possible to create a userscript which does things along the lines of what you've described. You'd need to decide exactly what you want and how you want it to look on the page.
- Do you want to always automatically include some specified text when you select the input box for an answer or question, or only when you begin a new question or answer (perhaps only on some SE sites)?
- Do you want to have a user-adjustable set of auto-text, similar to what's done for comments and custom close reasons by AutoReviewComments - Pro-forma comments for SE, which also has the ability to download comment sets from a URL.
- Do you want to add a button or buttons to the edit controls for the questions/answer creation/edit boxes?
If so, you might want to look at Magic™ Editor (GitHub) (install) to see what's necessary to detect the edit box and insert a button in those controls.
There are other userscripts that insert an icon in there, which might be easier to take code from. Magic Editor is just one that I use, so it came immediately to mind. It looks like the MathJax Buttons userscript you found on Stack Apps also inserts buttons in the edit interface. I haven't used it, so I'm not sure if it's up to date with SE's code changes and/or that it does a good job of detecting inline/in-page editing, etc. It looks like it was last modified in 2014, so it might be a bit dated at this point.
This is probably the solution which I'd choose, if I was implementing for myself what I think you're describing. However, I already have a clipboard manager installed, so the choice to use it has a low barrier to entry. I should probably also note that a clipboard manager is a program I almost always install on any machine I'm going to be using for a while, as the expanded features are something I use many times every day. So, my choice of this solution my be a bit biased by how I use windowing systems.
A clipboard manager is a program you install on your computer which significantly increases the functionality of your windowing system's clipboard. There are a significant number of different programs to choose from which will add a variety of features. For what you've described, the feature you'd probably be most interested in goes by a few different names, but I usually see it called something similar to "stickies".
"Stickies" allow you to pre-define text which will always be quickly available through an enhanced interface for your computer's clipboard, in addition to, or as an alternate to, the normal clipboard operation. How each program implements it is slightly different. Personally, I find having this capability quite valuable to hold text I commonly use in various different programs. I do have some stickies defined with text I commonly use when editing on Stack Overflow (e.g. to define code syntax highlighting, use code snippets, etc.). For what you've described, defining a "sticky" with the text you want would likely be my go-to solution.
You'll need to do a search for clipboard managers, but limited to the operating system you use. I'd suggest going through some sites which offer comparisons in order to find one that fits your needs. Then try it out and switch to another one if the one you first picked doesn't really do what you want.
For Windows, I use ClipX (WikiPedia) (main site). However, I can't recommend it at this point, because development stopped on it in 2008. It does still work. With it's available plug-ins, it has the features I'm looking for, but may not continue to work in the future. I use it because I've used it for years and am familiar with it. For someone who isn't already invested in it, I'd recommend doing some research to find a clipboard manager which fits your needs and is still maintained.