Moved mine between the end of reception and Y1 - not because of a house move but because the school was turning out to be, to put it politely, not the right place for them.
Actually I'd say don't overthink it - if you can get them in to visit or move just before the end of the year that might work better but the priorities for DD1 (who has a lot of anxiety about transitions) were knowing what the playground looked like (and eyeing up their trim trail she fancied the look of) and what colour uniform she was going to be wearing... the rest of the stuff the average adult frets about endlessly really didn't bother her.
It’s really not an issue at that age - dd moved to school 1 halfway through preschool year, then halfway through reception to school 2 - then 4 months later - moved to a school 3 at the beginning of Y1.
At each school she had a new “best friend” within a couple of weeks of starting. The similarities between schools are often much bigger than the differences and she always adapted no problem.