To the best of my knowledge, there are only a few things that can be saved to the Home Screen.
Apps
Folders
Widgets
Shortcuts
URL's (usually from websites)
It is at least theoretically possible to save an email to the Home Screen as a URL. I've never seen that ability in Mail. As Jupiter7 says, Mail does not even have a Share Button, where that option is normally found.
I am less familiar with the Gmail app, or the Gmail website. I looked over both, trying to find the option. Add to Home Screen is the usual name. That doesn't mean the option was never there, just that I can't find it now. There could be a couple reasons for that. One is that Gmail has removed the option. The other is that the option is no longer on the Gmail website in Safari.
You can Add To Home Screen the entire Gmail site using Safari's Share Button, but that won't save just an email, but the entire site., though it should open to the email saved.
Note, that if you leave the Open as Web App button on when doing so, it wont' look or work like Safari, but it is still Safari. Just without all the controls.
Another Note. The screenshot I'm sharing is from the iPadOS Public Beta, so it may not look like how you expect. Also, on there the Public Beta, the list of options shown don't come up automatically. You have to select the More (three dot) icon.
Third note. If you are saving emails as URL's on the Home Screen, you'll want to keep in mind you are not actually saving the emails. You are only saving the links to the emails. If you have no internet access or lose your account somehow, those emails are lost. They are not stored on your iPad.
I don't know if this helps, or if I'm make all the wrong assumptions. If so, please give a details step by step description of what app and steps you took to save emails to the Home Screen. With that maybe i can guess what is going on.