In the past, several SSD manufacturers had bugs in their firmwares. So to be sure that I can fix such issues with a newly bought SSD, I need some secure (and somewhat easy) way of updating the firmware.
I don’t need to do the update on my own Linux installation. A bootable ISO would be fine, too.
Which manufacturer has some well supported way of updating SSD firmware, even if I don’t have any Windows installations left?
Not for a SSD. Every manufacturer has some tool to update SSD firmware. Some Samsung models can actually be updated with fwupd but I’m unsure if this covers all Samsung SSDs or only the “Pro” series. I also tend to prefer booting into some dedicated “update ISO”, first, just to be sure that nothing interferes with the update.