I suggest that there is **no** quantifiable answer to your excellent question, because your first premise re critique of Copenhagen is correct, i.e. the wave function cannot actually collapse. 

Many people have gone into detail of course, but for me, the clearest and easiest to understand is [Adami][1], who not only has a paper going into all the detail you could ever want, but who has also proposed an experiment to prove it.   

Quote: '*It is silly to call [H. Everett's] relative-state picture a "many-worlds" interpretation, because it does not propose at all that at every quantum measurement event the universe splits into so many worlds as there are orthogonal states'.*  

**EDIT**:  Glick and Adami's proposed experiment (see above) has now been carried out, using quantum optics at the University of Ottawa, apparently **ruling [out][2] the collapse-picture by a wide margin.** These results are being [written][3] up (May 2021) 


  [1]: http://adamilab.blogspot.com/2016/03/on-quantum-measurement-part-7-there.html
  [2]: https://physics.stackexchange.com/questions/390942/is-the-copenhagen-interpretation-falsifiable
  [3]: https://physics.stackexchange.com/questions/561880/published-claimed-falsifications-of-objective-collapse-theories/561938#561938