2013 iMac supports the much-newer Catalina (6 generations newer than Mavericks)
If DriveDX reports problems with your internal SSD, then you have the option to replace that SSD (and the "fun" of removing/cleaning/retaping/etc. the display, simply to replace the SSD). OR... you can leave the bad SSD in place, and use an external USB SSD, where you install everything, ignoring the internal SSD completely.
One other thing... Your Samsung 870 EVO SSD came with a 5 year warranty. SO... If it is less than 2 years old, that might be a good reason to go ahead with replacing the internal.
A final point: Internet, for you, is probably full of "headaches" on Mavericks. Think of those errors, when sites that used to work easily for you, now are a struggle, if you can use them at all, particularly those that need log-ins, like on-line banking, etc. Your iMac would have a working internet again, simply by updating to latest (for your iMac) Catalina