My feeling is that THE PLANET will survive ok, but the human race (and maybe most other lifeforms) may not.
In what form the planet survives is highly debatable. A lot depends on whether you subscribe to the options (?) of::
(a) We will screw it all up and make the place uninhabitable for humans. That could also include some global epidemic as well as climate issues.
(b) There will be some sort of mega disaster eg the asteroid
impact type (as has happened many times before and which statistically is overdue)
(c) The good old Earth will decide to "do it's own thing" with or without intervention from the human race eg VERY little is needed to initiate a new Ice Age which could be of the minor (last one) type to which some of the human race could adapt, or the mega type - which would be equivalent to a global re-boot. Earth has done this several times in the past and ALL of the History
of the human race has happened in one of the placid bits that occur between ice ages.
WE are but mere specs in the timeline. At my age I am certainly not going to worry