fish shell. How to check if a variable is set/empt

How can I do something like

set variable (some_command_that_may_return_a_string)
if [ variable is set ]
    do_something

and inversely how do I check if the variable is empty?

set -q var (note the missing "$" - this uses the variable name) can be used to check if a variable has been set.
set -q var[1] can be used to check whether the first element of a variable has been assigned (i.e. whether it is non-empty as a list).
test -n "$var" [fn0] (or [ -n "$var" ]) can be used to check whether a variable expands to a non-empty string (and test -z is the inverse - true if it is empty).

These will be true/false in slightly different circumstances.

When no set var has been performed at all (and it has not been inherited from the parent process), set -q var, set -q var[1] and test -n "$var" will be false, test -z "$var" will be true.

When something like set var has been done (without any additional arguments), set -q var will be true, set -q var[1] will be false.

When something like set var "" has been done, both set versions will be true.

When something like set var "somestring" (or even set var "" "" [fn1]) has been done, the sets will be true and test -z "$var" will be false.

[fn0]: You never want to use test (or [) without quoting the variable. One particularly egregious example is that test -n $var will return true both if the variable contains something and if it is list-empty/unset (no set at all or set var without arguments). This is because fish's test is one of the few parts that follow POSIX, and that demands that test with any one argument be true. Also it does not handle lists properly - test -n $var will have weird results if var has more than one element.

[fn1]: This is because a list will be expanded as a string by joining the elements with spaces, so the list consisting of two empty strings will expand to " " - one space. Since that isn't empty, test -z returns false.