I don't see anything about qr//x that makes regexes built this way less vulnerable to the kind of exponential backtracking problem under discussion here.
I do see a great opportunity to, by assuming interpolated qr// substrings have the locality the syntax falsely suggests, inadvertently create exactly that kind of mishap with it being minimally no easier, and potentially actually more difficult, to notice.
Write your code however you like, of course, including concatenating strings and passing the result to 'eval'. The last time I dealt with more Perl than a shell one-liner was around 2012, and that the language encourages this kind of thing is one of the reasons I'm glad of that.
Given that I write my code with a text editor that does nothing but concatenate strings that I input and then I pass it to a compiler or an interpreter, all of the code I write is concatenating strings and passing it to 'eval'.
And I use proper decomposition to keep it cognitively manageable. It's pretty clear that reasoning about composition is beyond you, but trust me that given two procedures that both do not have an undesirable property, one can rest assured that simple composition will not introduce that undesirable property.
Many things are beyond me. Perhaps it's to my good fortune that the generally low utility of gratuitous personal insults is not among them. Certainly the next technical discussion I see improved by such behavior will be the first.
Well then, in the interest of amity let me suggest that it would be to your good fortune to work on your self-awareness. But, should you prefer not to, then by all means, you do you.
Regexes are code.
Therefore, decomposition makes complex regexes both feel and actually be easier to reason about.