SMART status is a capability that was intended to detect Bad Blocks and a few other problems on a Drive before they cause an outage. It is only very rarely effective, and is of extremely limited usefulness. If your drive does not support it, that is no great loss. In most cases (including yours) Drive problems appear before SMART status indicates a problem. So do not anguish over SMART status not supported.
Disk Utility "Repair Disk" or "First Aid" deals ONLY with the self-consistency of the Directory on your Drive. Passing that tells you NOTHING about the blocks that hold your data, as they are not read AT ALL.
But based on:
"My Mac became too slow, apps are crashing, Safari don't even open, and there is long-time beach balling"
run Etrecheck then and the report says that the there is drive failure.
you DO have a drive problem.
Backup Drive:
The first question is whether you have a Trusted Backup of your files. If you do not, the first thing you need to do is buy a large external drive (recommended 3x the size of what needs to be saved) and enable the Time Machine software that shipped with your Mac. A 3.5-in desktop drive with its own power supply may allow you to choose a larger drive for less money. This drive does not need to be fast.
Replacement Internal drive:
You may also need a new Internal drive very soon. Many Users in your situation would suggest an SSD drive, but that is your choice. A regular 2.5-in rotating drive to fit inside your Mac would work fine. You are likely to need an external enclosure or adapter to get MacOS installed before you swap it with the internal drive. This separates problems from rescuing data from problems of the transplant.
