Potential to experimentally "verify" many worlds interpretation?

[vlaiv]

I've just seen latest episode of PBS Space time:

https://www.youtube.com/watch?v=BU8Lg_R2DL0

Which "explains" how many worlds elegantly gives rise to Born's rule. Main objection that I have on this interpretation (which I think is extremely elegant otherwise) is reiterated.

Just to sum it up:

If we have say 1/3 to 2/3 probabilities of outcome of some event (two possible outcomes) - there will be three copies of the world: one copy with first outcome and two copies with second outcome.

My objection is - this violates Occam's razor - if we have 0.0001% vs 99.9999% probabilities instead we would need something like 9999999 same copies of the world to explain it. That is just a bunch of unnecessary copies, don't you think?

But my objection goes deeper than this. I'm certain that we can prepare photon polarized in such way that probability of it passing thru polarizing filter is sqrt(2)/2 for example.

See the problem? No amount of worlds can provide this probability as it is irrational number and can't be written down as quotient of two integers - so no matter how many copies you have - you can't reproduce Born's rule.

This got me thinking - maybe this is a way to experimentally confirm many worlds?

If we can't prepare photon in such way (or electron - or any other setup) to have irrational number as probability - that might be step in the right direction to verify many worlds (how ever crazy it may seem with huge number of same copies).