It might help to know that the "maths age" number is not the same kind of measurement as the standardised score her school reports, so you are not really comparing like with like. School assessments are usually reported against a national standard where 100 is expected for her year group. Maths Whizz's maths age is its own internal scale, worked out from how she performs on its own question bank. Both can be perfectly valid and still disagree, because they are not measuring the same thing.
Your summer born theory is partly right, but I think the bigger factor is what each one is actually testing. Adaptive apps tend to measure fluency, so recall and procedure, on fairly tightly defined question types. School work from Year 4 upwards leans much more on reasoning and multi step problems, which is the bit most children find hard. A child can be genuinely quick on the fluency side and still find the reasoning papers tricky, and that gap is very common. It probably also explains why she tells you she struggles even though the app says she is ahead; she is comparing herself against the harder thing, not the easier one.
The bit I would actually pay attention to is that nothing has got harder in a few months. Adaptive apps deliberately sit a child just under their frustration point to keep them coming back, which is sensible in itself, but if the difficulty has genuinely flatlined then it has stopped stretching her rather than the other way round. Worth checking whether there is a setting that lets her work above her assigned level.
If you want an independent read, the past SATs and end of year papers on the gov.uk site are free to download and will give you something directly comparable to what school is telling you. My DH built mathstutor.me, and the free assessment on there reports against the actual national curriculum objectives year by year rather than giving you a single maths age, so you can see which specific topics are secure and which are not. I found that far more useful than one number. It runs from KS1 up to GCSE and the free tier is 8 exercises a day, so you can try it alongside Whizz without cancelling anything. Obviously I am biased, so take that bit with a pinch of salt; the free papers suggestion stands on its own.
One last thought, more as a mum than anything else. If she keeps telling you she struggles while her assessments come back perfectly fine, that is very often confidence rather than ability. Our DS did exactly that for a good while, and what shifted it was him being able to see his own progress laid out rather than us just telling him he was doing fine.