I am curious how these interventions are done. I was a reading tutor for a year and they had a very specific protocol for what they wanted me (and other tutors) to do. There was some phonics training for younger kids in K-1st grade but with 2nd/3rd it was mostly having them read portions of passages and correct them when they made a mistake (or tell them the word if they didn't know) and then have them start the sentence over. Repeat over and over until the student was reading the passage fairly fluently with very few mistakes. They also had "duet reading" where I read one word, student read the next, etc, and eventually the kid read the whole thing on their own. But I wasn't teaching them phonics. The younger kids had specific interventions to learn letters and letter sounds and how to do simple blending to read nonsense words, but once a kid was in the 1st grade, that pretty much stopped. I am pretty sure that I had some older kids in 2nd-3rd grade with dyslexia or something similar. They just never seemed to improve much and while they might have become fluent with one passage it didn't necessarily transfer to other reading.
i remember one third grade girl who had trouble reading basic nonsense words like bab or cox, or whatever. She was not fluent with them and made a lot of errors. (and no, the school would not evaluate her even though I kept nagging, because she was meeting the minimum cutoffs in terms of overall fluency on CBM type fluency passages--probably because she was gifted).