Upgrade to FCP X

Well, I finally broke down and upgraded my iMac (21.5-inch, Late 2013, 2.9 GHz Intel Core i5, 8GB RAM with 3 external hard drives) to the latest OS Mojave 10.14.5. I hope this was not a mistake, as I have edited dozens of video projects using FCP 10.0.9. Of course, now I am prompted to upgrade to the latest version of FCP, because my current version is not compatible. (Before upgrading my OS, I used Time Machine to back-up all the data on my start-up drive) Will I still be able to access my earlier completed projects using the latest version of FCP?

Well Greg, thanks for all the helpful information.
I've just spent about one hour on the phone with Apple Support! I'm not sure what their policy is regarding upgrades of Final Cut Pro, but we're about to find out. (They disconnected my call!) The Apple App Store won't let me upgrade my FCP, it wants me to purchase FCP, which I already have. So they are trying to figure out why it won't let me just convert to the latest version.

Meanwhile, I hope I can return to elements of former projects, but it's not imperative. I have them all saved as QT files, so I can always drop them in a timeline, if necessary, and massage! BUT I do produce a weekly half-hour TV show, so I would really like to retain my titles, commercials, background music, etc, for next week's show!
I'll keep you posted on what solution Apple comes up with.

Thanks Again!

Phil (Mister Pie)