I’m familiar with sectoral bargaining in the abstract but wasn’t aware European workers had the ability to choose which union represented them in negotiations. How does that work in practice?

Not only in Europe, but in Canada too. Think of the union as a corpo offering bargaining and administrative services. Unions compete with each other for workforces. The typical case would be for a newly unionizing workforce needing to choose which union to join.

It is rare, but a workforce can even choose to move to a different union.

Depends on the country.

In a lot of countries, it's not much different than choosing a pension fund option. You join a job, you choose which union best represents you based on your industry/title/etc (if you are not already a member). If you are not happy with your current agreement, you choose a different union that promises better outcomes.

It's so much less extreme than US unionization. There's not much reason for hostility between business and unions - unions don't get these all or nothing powers like they do in the US.

It is common for big workplaces to have multiple unions and essentially all unions are sectoral and role-specific rather than company specific.

Take the NHS; it will have to deal with ten plus separate unions - https://nhsunions.org/#about – of which the biggest powers are the British Medical Association and the Royal College of Nursing, but the cleaners are GMB or Unite and they're huge pan-working-class institutions.

Education has to deal with the NEU, the NASUWT, and the NAHT, each of which has a different political slant. Some unions in the UK have been historically rather centrist in their politics (a good example of that is Prospect, https://prospect.org.uk/about/, which is a roll-up of a number of scientific and finance unions), some are firebreathing communists, but all of them work across employers.

There's also no such thing as a closed shop in the UK – because there are much stronger worker protections, there's less of a need for one.

(I was, at one time, in a majority-UCU workplace; https://www.ucu.org.uk.)

It depends heavily on the country but a worker at a company can pick a union to represent them. You might see a billboards saying join Union a or Union B. If you Union a is corrupt or screwing over one group of workers in favor of another group of worker, the laborers will just leave it and go to a different one.

This solves a lot of problems with us unions, where they have a state sanctioned Monopoly on the workers.

The classic example is unions are going for terms that screw over junior members but there are other perverse examples. At my friend's company the Union demanded that it be forced to return to office because the larger number of field technicians we're a voting majority of the union and angry they couldn't work from home.