I just took a look at All in One SEO Pack and it has been tested to 5.0.3 which is the latest, greatest WordPress version so far.
As to your host not supporting the Classic editor plugin… they were probably talking about help desk support for the editor itself or the plugin but the Classic Editor plugin should run just fine for you.
Also, the security updates are for WordPress – not the Classic Editor Plugin itself. 4.9.8 and 4.9.9 still support the Classic Editor natively. You can run the Classic editor plugin also but you don’t need it until you move up to 5.X.
It’s possible your theme won’t work but having the Classic Editor enabled before the update to 5.0.3 will probably keep the problems away. You might even find the Block Editor will work fine with your theme. There’s an option for switching back and forth between the two editors with the Classic Editor plugin installed.
If you decide to try 5.o.3 then enable the Classic editor plugin just before you upgrade. Make sure you do a complete backup including the database just in case.
I suggest you do the upgrade to 5.X sometime in the near future and I’ll tell you I upgraded two sites that I held back on until 5.0.3 came out yesterday. It went smoothly and the Classic Editor was there waiting for me when it finished.
You should be able to manually update to 4.9.9 from the dashboard if you want to do that but the automatic update should have happened if not blocked by a setting.
I’m not a real big fan of automatic updates!