While Sauron's spirit is technically still alive, it's too weak to ever do anything, now or in the future. Whatever is left is entirely devoted to his hatred and not free to act.
As you've pointed out, Gandalf says that:
...his fall will be so low that none can foresee his arising ever again. For he will lose the best part of the strength that was native to him in his beginning, and all that was made or begun with that power will crumble, and he will be maimed for ever, becoming a mere spirit of malice that gnaws itself in the shadows, but cannot again grow or take shape.
The Lord of the Rings - Book V Chapter 9 - "The Last Debate"
Shortly after publication Tolkien stressed this same point in a letter. Sauron can no longer rebuild.
...the spirits so often took the form and likeness of the Children, especially after their appearance. It was thus that Sauron appeared in this shape. It is mythologically supposed that when this shape was 'real', that is a physical actuality in the physical world and not a vision transferred from mind to mind, it took some time to build up. It was then destructible like other physical organisms. But that of course did not destroy the spirit, nor dismiss it from the world to which it was bound until the end. After the battle with Gilgalad and Elendil, Sauron took a long while to re-build, longer than he had done after the Downfall of Númenor (I suppose because each building-up used up some of the inherent energy of the spirit, which might be called the 'will' or the effective link between the indestructible mind and being and the realization of its imagination). The impossibility of re-building after the destruction of the Ring, is sufficiently clear 'mythologically' in the present book.
June 1957 Letter to Major R. Bowen (Letters of JRR Tolkien #200)
Around April 1959, Tolkien wrote an essay comparing Morgoth and Sauron. In it he discussed the nature of how while spirits cannot be destroyed, they can still be reduced to the point where their will power was less than what was required for their obsession, and thus no part of them is available to focus on healing themselves. Tolkien says that with the destruction of the ring Sauron was reduced to this state, though Morgoth was not.
Melkor was not Sauron. We speak of him being 'weakened, shrunken, reduced'; but this is in comparison with the great Valar. He had been a being of immense potency and life. Elves certainly held and taught that fëar or 'spirits' may grow of their own life (independently of the body), even as they may be hurt and healed, be diminished and renewed. If they do not sink below a certain level.
Since no fëa can be annihilated, reduced to zero or not-existing, it is no[t] clear what is meant. Thus Sauron was said to have fallen below the point of ever recovering, though he had previously recovered. What is probably meant is that a 'wicked' spirit becomes fixed in a certain desire or ambition, and if it cannot repent then this desire becomes virtually its whole being. But the desire may be wholly beyond the weakness it has fallen to, and it will then be unable to withdraw its attention from the unobtainable desire, even to attend to itself. It will then remain for ever in impotent desire or memory of desire.
The dark spirit of Melkor's 'remainder' might be expected, therefore, eventually and after long ages to increase again, even (as some held) to draw back into itself some of its formerly dissipated power. It would do this (even if Sauron could not) because of its relative greatness. It did not repent, or turn finally away from its obsession, but retained still relics of wisdom, so that it could still seek its object indirectly, and not merely blindly. It would rest, seek to heal itself, distract itself by other thoughts and desires and devices — but all simply to recover enough strength to return to the attack on the Valar, and to its old obsession. As it grew again it would become, as it were, a dark shadow, brooding on the confines of Arda, and yearning towards it.
"Notes on motives in the Silmarillion", incorporating marginal note 11 (Morgoth's Ring, Myths Transformed Text VII)
And in a 1968 interview Tolkien says that "very little existed", though that he still wouldn't have liked to meet Sauron in that state.
Of course, there’s another thing, yes, yes, that is a power, yes, yes. People who’ve met some of the great characters [get] a sense of something which is nothing to do with them or their intellectual power. Yes. I wouldn’t have liked to meet Sauron when his Ring had been destroyed, very little exist[ed?]. [But] one does meet people like that. Fortunately the people I’ve met with this extraordinary will-power, which is quite unrelated to [any?] ideas, have nothing. Fortunately when I’ve met them they were fortunately not people with any particular desires, ambition or even sufficient intellect [?].
""Tolkien in Oxford" (BBC, 1968): A Reconstruction." (Tolkien Studies 15)
