What is the word for "wondering if what you're doing is pointless"?

I suggest:

The futility of completing these tasks.

Lexico gives

futility
NOUN

Pointlessness or uselessness.

Merriam-Webster has

futility noun
2 : a useless act or gesture

Thucydides describes the futility of any human response: Appeals to the gods and the work of doctors – who died in droves – were equally useless.

Meaninglessness is probably a good fit. The "preacher" in the book of Ecclesiastes, Chapter 1, in the Tanakh, said numerous times "Meaningless! Meaningless!" Older versions read "Vanity of vanities . . . all is vanity." The first 11 verses capture your feeling quite well, I think.

1 The words of the Teacher, son of David, king in Jerusalem:

2 “Meaningless! Meaningless!” says the Teacher. “Utterly meaningless! Everything is meaningless.”

3 What do people gain from all their labors at which they toil under the sun?

4 Generations come and generations go, but the earth remains forever.

5 The sun rises and the sun sets, and hurries back to where it rises.

6 The wind blows to the south and turns to the north; round and round it goes, ever returning on its course.

7 All streams flow into the sea, yet the sea is never full. To the place the streams come from, there they return again.

8 All things are wearisome, more than one can say. The eye never has enough of seeing, nor the ear its fill of hearing.

9 What has been will be again, what has been done will be done again; there is nothing new under the sun.

10 Is there anything of which one can say, “Look! This is something new”? It was here already, long ago; it was here before our time.

11 No one remembers the former generations, and even those yet to come will not be remembered by those who follow them.

Then again, perhaps you have a mild case of nihilism, which is defined, partially, as "the doctrine that existence or values are meaningless." You have the feeling that your efforts are in vain and pointless.

Some other words, which are somewhat synonymous with nihilistic or meaningless are:

negativistic

pessimistic

questioning

cynical

apprehensive

unsettled

uneasy

aporetic

unsatisfied

lacking confidence

wondering