Triton's orbit is decaying due to tidal interactions, it is predicted to reach Neptune's Roche limit in about 3.6 billion years (Chyba et al., 1989) where it would likely be disrupted, possibly forming a ring system. This timescale is shorter than the timescale for the Sun to become a red giant.
Even before that, Triton's orbital decay will bring it into the region of the inner prograde satellites. There's a possibility that it could experience one or more major collisions (since Triton is in a retrograde orbit, the collision velocities for an impact with a prograde satellite will generally be higher). Such collisions would likely have an effect on the inventory of volatiles on the surviving objects.
This makes prediction of the future evolution of conditions on Triton extremely difficult.
Even if this weren't the case, there would still be a question of whether a world as small as Triton could maintain liquid water. Arnscheidt et al. (2019) provide a conservative estimate for the lower gravity limit for waterworlds to maintain a stable atmosphere at around 1.48 m/s2. Triton's gravity of 0.78 m/s2 is below this threshold, putting it in the non-habitable "comet-like" regime. They also note that deglaciation of an icy world into a long-lived habitable state is unlikely: except at very low albedos, the required stellar flux is sufficiently high that the moon transitions directly to a short-lived, high temperature state.