I have been wondering if there could be any improvement in performance or whatever else, if I reused my old SSD. Basically drive is no longer useful for me, it's small, I have no use for it, don't want to recycle, because it works and not worth selling, as it is worthless. It's Samsung 840 Evo SSD (SATA). Would it do anything at all?
It really depends on the performance of your current primary drive and your individual usage case(s).
When solid state storage first emerged, it was too cost prohibitive for people to install a full operating system on it, so some used it in the manner you describe or as a scratch disk for certain tasks.
Later there were hybrid SSD-HDD combos design to speed up performance by putting more frequently accessed disk data on the faster SSD. Apple called this a Fusion Drive and it existed a handful of their desktop Mac models for a period of time.
I usually have multiple SSDs in my systems: m.2 NVMe Gen4 (always the boot drive), m.2 NVMe Gen3 (a secondary drive) and SATA SSDs (a tertiary media drive). There are some external 3.5" HDDs that are really just used for offline file storage (video files, old photos, game backups, etc.).
The best thing to do is to try it out yourself and see if there's any tangible benefit for your usage case. What might work for Person X might not work for you and vice versa.
If you have a large amount of RAM, your system is probably writing to the pagefile less frequently. Remember that SSDs aren't like spinners where the drive head can only be at one place at one time. Multiple simultaneous operations can happen on an SSD and there's no seek time involved like the old spinners.
For one of my older, smaller SATA SSDs, I ended up putting it in an extra enclosure for shuttling around files between systems. This external SSD has much faster transfer rates than SDHC cards or USB thumbdrives.