As of this merge you can write:
try { let $foo .= bar }
This is a step short of what I think would have been an ideal solution, which is unfortunately a syntax error (due to a pervasive weakness in Raku's current grammar that I'm guessing is effectively unsolvable, much as I would love it to be solved):
{ let $foo .?= bar } # Malformed postfix call...
(Perhaps I'm imagining things, but I see a glimmer of hope that the above wrinkle (and many like it) will be smoothed over a few years from now. This would be after RakuAST lands for Raku .e, and the grammar gets a hoped for clean up in Raku .f or .g.)
Your question's title is:
Variable re-assign method result if not Nil
My solution does a variable re-assign method if not undefined, which is more general than just Nil.
Then again, your question's body asks for exactly that more general solution:
Is there idiomatic way of applying and assigning object variable method call, but only if it's defined (both method and the result)?
So is my solution an ideal one?
My solution is not idiomatic. But that might well be because of the bug I found, now solved with the merge linked at the start of my answer. I see no reason why it should not become idiomatic, once it's in shipping Rakudos.
The potentially big issue is that the try stores any exception thrown in $! rather than letting it blow up. Perhaps that's OK for a given use case; perhaps not.
Special thanks to you for asking your question, which prompted us to come up with various solutions, which led me to file an issue, which led vrurg to both analyse the problem I encountered and then fix it. :)