In my view, in the area of State aid, the term “non-regression” isn’t very helpful. I’d have the following questions about the EU position here.
The first question is about content. Is the EU going to demand that the UK follow the basic structure of the State aid rules: the question as to what counts as “aid” (and therefore falls within scope) being determined by EU case law over the decades?
With a sub-question: does the UK have to follow ongoing CJEU case law on that question? Even with no UK judge or presence on the ECJ?
Or could the UK devise its own system, based perhaps on the definition of a specific subsidy in WTO law? (The question of whether they are in fact very different is a nice one: but the UK may want the optic of a substantive change.)
Second question. What about policy? Does the UK have to follow EU policy on what aid can be cleared in (say) the broadband or aviation sector? Does the UK have to follow the EU view of how poor an area has to be for regional aid to be permissible?
If the answer is “yes”, how sustainable does the EU think that position is, when the UK is given no say in setting that policy?
Third question: what about enforcement? Is it enough to have an independent UK agency (CMA) (supervised by UK courts) + a joint committee/arbitration mechanism in case of disagreement as to whether a UK decision is acceptable?
Does the UK regime have to be actionable by private litigants in UK courts?
Must the CMA’s decisions on what is aid and what can be cleared be “marked” by the Commission and the CMA bound to take serious note of its comments (see the mechanism in the old NI backstop)?
NB that the EU’s position is stronger on this issue than it could be because Johnson has already sold a major part of the pass in the new NI protocol (without, I suspect, realising what he had done: dangers of negotiating technical material in a rush and without consultation).
With the result that divergence would force the UK to run *both* an EU *and* a UK set of rules, often applying both to the same measure.
(And with the EU rules enforceable in the UK courts and by the Commission as if the UK were still in the EU and with the boundaries and interpretation set by the ECJ.)
(See this thread for the details.)
And see Article 12(4) and (5) of the NI protocol for enforcement. 
To paraphrase Lady Bracknell: to operate one State aid regime may be a necessity: to run two at the same time looks like carelessness.
