How to rewrite this simple loop using assignment expressions introduced in Python 3.8 alpha?

Simple loops like your example should not be using assignment expressions. The PEP has a Style guide recommendations section that you should heed:

1. If either assignment statements or assignment expressions can be used, prefer statements; they are a clear declaration of intent.
2. If using assignment expressions would lead to ambiguity about execution order, restructure it to use statements instead.

Simple loops should be implemented using iterables and for, they are much more clearly intended to loop until the iterator is done. For your example, the iterable of choice would be range():

for a in range(10):
    # ...

which is far cleaner and concise and readable than, say

a = -1
while (a := a + 1) < 10:
    # ...

The above requires extra scrutiny to figure out that in the loop a will start at 0, not at -1.

The bottom line is that you should not be tempted to 'find ways to use assignment statements'. Use an assignment statement only if it makes code simpler, not more complex. There is no good way to make your while loop simpler than a for loop here.

Your attempts at rewriting a simple loop are also echoed in the Tim Peters's findings appendix, which quotes Tim Peters on the subject of style and assignment expressions. Tim Peters is the author of the Zen of Python (among many other great contributions to Python and software engineering as a whole), so his words should carry some extra weight:

In other cases, combining related logic made it harder to understand, such as rewriting:

while True:
    old = total
    total += term
    if old == total:
        return total
    term *= mx2 / (i*(i+1))
    i += 2

as the briefer:

while total != (total := total + term):
    term *= mx2 / (i*(i+1))
    i += 2
return total

The while test there is too subtle, crucially relying on strict left-to-right evaluation in a non-short-circuiting or method-chaining context. My brain isn't wired that way.

Bold emphasis mine.

A much better use-case for assignment expressions is the assigment-then-test pattern, especially when multiple tests need to take place that try out successive objects. Tim's essay quotes an example given by Kirill Balunov, from the standard library, which actually benefits from the new syntax. The copy.copy() function has to find a suitable hook method to create a copy of a custom object:

reductor = dispatch_table.get(cls)
if reductor:
    rv = reductor(x)
else:
    reductor = getattr(x, "__reduce_ex__", None)
    if reductor:
        rv = reductor(4)
    else:
        reductor = getattr(x, "__reduce__", None)
        if reductor:
            rv = reductor()
        else:
            raise Error("un(shallow)copyable object of type %s" % cls)

The indentation here is the result of nested if statements because Python doesn't give us a nicer syntax to test different options until one is found, and at the same time assigns the selected option to a variable (you can't cleanly use a loop here as not all tests are for attribute names).

But an assignment expression lets you use a flat if / elif / else structure:

if reductor := dispatch_table.get(cls):
    rv = reductor(x)
elif reductor := getattr(x, "__reduce_ex__", None):
    rv = reductor(4)
elif reductor := getattr(x, "__reduce__", None):
    rv = reductor()
else:
    raise Error("un(shallow)copyable object of type %s" % cls)

Those 8 lines are a lot cleaner and easier to follow (in my mind) than the current 13.

Another often-cited good use-case is the if there is a matching object after filtering, do something with that object, which currently requires a next() function with a generator expression, a default fallback value, and an if test:

found = next((ob for ob in iterable if ob.some_test(arg)), None)
if found is not None:
    # do something with 'found'

which you can clean up a lot with the any() function

if any((found := ob).some_test(arg) for ob in iterable):
    # do something with 'found'