// What Earthly business is it of the EU to determine whether or not we change our clocks twice a year? What difference does it make to anybody other than those in the UK? How does our changing clocks impinge on anybody else in Europe? //
Assuming the UK isn't planning to cut itself off from Europe altogether, then the EU will need to now what the time is in the UK, and vice versa. At the very least, then, the EU certainly cares about whether or not our clocks change: they'd need to know. Then the rest follows because it is generally easier to organise meetings and trade across time zones if those time zones are roughly aligned, and it can be a pain to keep track.
In the good old days, when time zone policy wasn't even a thing, every city kept its own time. This turned out to be a bit silly when cities started to be more easily connected to each other, so very quickly it was realised that cities needed to abandon the concept of local time and facilitate trade and transport by aligning their time zones.
The exact same principle applies to the EU. It is, incidentally, *not* a diktat: EU members just voted for it in Parliament. They were perfectly at liberty to reject the proposal, but as it happens the policy has broad public support across the EU members and citizens.
I get what you are saying about setting aside the merits of a particular policy, but in this case the entire point is to ensure that the EU is aligned as much as is feasible on a matter that it's worth coordinating across states anyway.