Europe, including the UK, has effectively functioned as one country for a long time. Goods movement, business, workforces and families sprawl across borders. In early 2020, by the time people realised that the ski resorts etc were in trouble it was too late - the families were already home from half-term holidays.
The first lockdown did what it had to in the UK - stopped hospitals collapsing, and got some PPE to places that needed it.
The second/alpha wave lockdown was left too late in the UK, but ultimately bought a bit of time for the vaccine rollout to start. The earlier (regional) lockdowns in 2020 on the other hand were mostly ineffectual, before becoming resented and ignored.
Controls since the vaccine rolled out? Again, things that bought time for more vaccinations in undervaxxed groups - particularly during the Delta wave were useful.
In England, those official controls were mostly ceremonial. The real controls were being done by individuals and families who basically did not go back to business as usual. In Scotland and Wales they tried to do more, but vaccine passports, masks etc didn't seem to affect outcomes very much.
The only things that have really affected outcomes are vaccination and the actions that bought time for vaccination. I'm not sure what countries are buying time for now with border controls and lockdowns. If it's to keep hospital numbers manageable I understand it, otherwise no.
So this study's idea that lockdowns, school closures etc did nothing - no, I don't agree. In the first half of 2020 they were all we had. In the winter of 20/21 we needed to use them tactically to protect hospitals and start vaccinating.
If we hadn't vaccinated most of our vulnerable population before Delta arrived it would have been a nightmare, even if we used the lockdown card again.