How to extend the time that a screenshot remains on screen on macOS Mojave?

I know this is slightly off-topic and not quite a direct solution to your question, but this option may be of interest to you. You mentioned taking screenshots for tutorials… . I use Take screenshot selection, upload to imgur. + more cool things almost exclusively.

The imgur-screenshot utility, straight out of the box without configuring any options, uploads the screenshot to Imgur , opens a browser window of the uploaded screenshot (for easy access if you need to manipulate the image), copies the URL of the screenshot to your clipboard, and also stores a local copy of the image.

I actually created an AppleScript application, and included.. imgur-screenshot.sh into a script libraries folder in the application bundle…

on imgur_screenshot()
    set imgUR to (path to me as string) & "Contents:Resources:Script Libraries:imgur-screenshot.sh"
    set imgUR to imgUR as alias
    set imgUR to POSIX path of imgUR
    set imgUR to quoted form of imgUR
    do shell script imgUR
end imgur_screenshot

imgur_screenshot()

From here, with enhanced dictation enabled, I selected the new AppleScript application in Finder, and simply spoke the command “Make This Speakable”, and configured the newly created dictation command… now anytime I need to take a screenshot, I simply say “Upload Screenshot” which sets the whole process in motion

Instead of hitting return or capture when determining the window region you want to grab, enter command-C for copy.

Then command-V wherever you want to put it.

Haven't tried this method with full screen screenshot as I never use it.