Hard to say, but probably not a scam if you keep seeing it WITHIN Gmail.
"Storage space" means disk space belonging to Google, that Google lets you use -- probably for free, unless you paid to use more. It applies to all your Google applications under your login, so it includes Gmail, Google Drive, and anything else.
In Gmail with your message listing in view (e.g., with "Inbox" selected), scroll down to the bottom and look in the left corner under the list of messages. (Not under the far left column of Labels.) It says how much storage you are using in all your Google applications.
"xx.xx GB (yy%) of 17 GB used"
So 17 GB is the amount Google lets you use, and apparently either you are close to that limit, or the messages you saw are a scam and not from Google. This line should answer that question.
I have YEARS of email messages, many with attachments, and it all adds up. I don't think there is a way to easily show the amount of space that is "ordinary" text messages versus bloated HTML messages (almost no email messages are plain text anymore) versus messages with attachments.
If you go to Accounts, I think there's a way to "purchase" more storage space. It's probably an annual fee. I've not done that. Just saying that I think it's still a possibility.
Otherwise, it may be time to manage your old emails better. Gmail's mantra used to be that there was no need to delete emails, but it was also true that the amount they allocated to users was constantly increasing. A long time ago they stopped doing that, but they also made the cap somewhere in the 15 GB range (though I guess it's now been increased to some 17 GB).
By the way, "Archived" emails probably doesn't mean what you think. ALL it means is they are no longer in your "Inbox" view. All your messages together, archived or not, adds up to your total usage.
Regards,
Andy