Educational researcher here. There's no such thing as a "science of reading." It's part of the highly politicized "reading wars" (see also the "math wars" which has been going on for decades). It's no coincidence that Republicans are pushing phonics as the end all be all solution to teaching reading, and you can cherry pick educational research studies that support or disconfirm various teaching strategies. Phonics has its place, contexts where it is appropriate and beneficial, but it is not the sole strategy that works or should be used in every context.
The good news is there are a lot of strategies that help with reading in various contexts. There's even research on how reading to dogs (or even robots) helps students with reading :)
I notice that the study you cite is measuring effectiveness in reading interventions. Obviously, that's where the data is coming from because we don't carefully track readers who learn successfully at a much earlier age.
However, I wonder if the ideal pedagogy would be different for younger students (maybe pre-K to 1st) who have less knowledge and smaller vocabularies? It's a bit tricky because a lot of the students who need intervention probably need remedial instruction in other areas too, but some of them may have been good students who struggled with reading.
A recent meta-analysis https://www.researchgate.net/publication/338494581_Meta-Anal... and the What Works Clearinghouse have summaries of the evidence for different strategies for improving early reading skills: https://ies.ed.gov/ncee/wwc/practiceguide/14 Direct Instruction (also championed by one political side) is not an effective strategy: https://ies.ed.gov/ncee/wwc/EvidenceSnapshot/139
Here's just one post with a little more info on the political context: https://radicalscholarship.com/2023/01/14/does-the-science-o...
A bigger scandal is how states like Florida game the system to make their reading score rankings look higher: https://www.tampabay.com/opinion/2023/01/05/floridas-educati...
The good news is there are a lot of strategies that help with reading in various contexts. There's even research on how reading to dogs (or even robots) helps students with reading :)