This notification is simply a statement of fact. The UK government plans a bill to retain EU law for the transition period. The ECJ retains authority over certain matters in the transition period and any transition from EU oversight takes place gradually after that.
BUT ... none of this has been agreed yet. Both the EU and the UK would lose out significantly unless these matters are settled. The assumption is they will be settled. After all, disruption on this scale is unthinkable to both parties.
BUT ... they aren't settled yet (or even remotely close to being settled) and we really need to get on with this to avoid chaos.
In my personal opinion it will be impossible to do anything other than accept EASA for now. Our pre-EASA bi-lateral agreements no longer apply. Bi-lateral negotiations, open skies agreements etc. will take a long time - there is nothing we can do about other countries parliamentary timescales - and that assumes the political will is there.
I think EASA in some shape or form with ECJ involvement in some shape or form is pretty much inevitable.