SSDs may actually worse than HDDs, depending on what NAND chips are in use. Although there are no moving parts to seize up, they do require an occasional power up because they represent data via voltage levels and we have not yet found a perfect insulator (meaning they will inevitably leak charge), and with QLC being all the rage these days (4 bits represented in each cell using one of 16 discrete voltage levels), when the voltage levels start to degrade, it could easily cause catastrophic bit rot.
How long a given SSD will last before losing data depends on the chips it is built with. I remember reading that Sandisk rates their flash storage as being able to survive a year without power (though I read that years ago and cannot find a source for it now), though [0] says 2-5 years, so technology has likely advanced since I last read about this. Either way, you should probably try and power up your SSDs at least once a year to keep the cells charged. This is less work than to keep an HDD healthy for cold storage, but it certainly isn't "set and forget" like tapes or optical disks.
Edit: I remember pulling my first SSD, a 60 GB Intel 330, from an old laptop and, despite having not been powered on for 3 years, it still booted. But that was MLC/DLC [1], which only has 4 voltage states, and I only saw that it booted, not that all my old data was intact.
[0]: https://www.easeus.com/resource/does-ssd-need-power.html
[1]: https://www.intel.com/content/dam/www/public/us/en/documents...