Yes, clearly all gods are truly immortal, unless their religion says they are not. Some gods can die. But to truly die they have to die on EVERY plane of existence, as long as there is belief somewhere, that the god exists, then they still exist, possibly at a reduced level.
I’m just not going to impugn anyone by accident, better to claim a mortal god immortal than vice versa and get hit by Blue Lightning.
nasty stuff, Blue Lightning.
It is all very complicated and depends on the pantheon.
But realize this, even then it is not so simple. Some pantheons establish different rules on different planes of existence, and even within the same plane they may move between cultures and change/mix things up. The Egyptian gods were really big on this. If you follow them over time and in both lower and upper Egypt, you see the same or similar beings sometimes they are separate people other times it’s just a name change, sometimes two deities are parent child sometimes lovers–husband and wife—
The thing is, these gods stick around for a long time, and they will change their PR tactics and branding to adjust to the time and place. They will try different marketing strategies. Change their names, their roles etc.