First, I’ve never made this particular “recipe”, so take whatever I say about it with a grain of salt. Second, when I have used rye flour, I don’t think I can remember ever going over about 20% and that has been enough to both make for an interesting flavor addition and also make the dough pretty sticky, hard to handle, and not hold its shape very well.
I think that sourdough bread is both similar enough and different enough from commercial yeast bread that having experience with the latter can be a detriment to learning the former because certain things you have come to expect don’t happen the same way.
So I’d suggest a couple things. First, it might be worthwhile to try a more basic sourdough recipe like @eric’s sourdough no-knead bread. Having success or not with a simple recipe like that will rule out a lot of sources of potential problems.
If you are dead-set on doing this recipe, you could try changing the ingredients to 400g bread flour and 100g rye flour and then start with 350g of water and see how the dough feels when it’s all mixed up. Add more water a little at a time if it seems too dry. See how it works with a higher proportion of bread flour.
Aside from ingredients issues, getting a soupy dough that won’t hold its shape, or falls down in the oven can be the result of over-proofing with sourdough. So really keep an eye on the proofing process and make sure that you have a feeling for when the rise is peaking and err on the side of ending the bulk fermentation too soon rather than too late until you get to where you have enough feeling for it to hit it on the head exactly.