Please give me some examples of "next to" when it means "almost", as in 'Reaching an indisputable answer is next to impossible'.
I'd appreciate if I come to know if this kind of things used often too. Thanks.😎

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Almost is used more commonly, but "next to" is also a pretty common phrase.
It is not as versatile as almost, and in all my examples except "next to godliness", "next to" could be replaced by "almost" and the meaning wouldn't change.
Also, I think that there are only a few phrases in which "next to" can be used.

one of the most common is "next to nothing"
I know next to nothing about stem cells.
I earned next to nothing.
We can do next to nothing to help her.
This box of flamingo eggs costs next to nothing.

"next to impossible"
Understanding what she's saying is next to impossible.
It's next to impossible to fill out this test correctly.


"next to no time"
I'll be there in next to no time.
The house burned next to no time.

These are the phrases I can think of. It is possible that there are more, but these are probably the most common.

This is an idiom:
Cleanliness is next to godliness.