There are exceptions, in established shipping (and a few other types of) channels, the sailboat does _not_ have right of way. Also, when sailboats are using their motors for power they are considered motorboats and the special right of way no longer applies. It is also very rare to see a sailboat under sail power in a harbor and large commercial ships are always manually piloted in a harbor.
Assuming they can see you, the captain of a large boat will try to give way rather than squash you (they'd be _super_ angry about having to do so, though), but in practice they're already hugely under-crewed, so there's a large percentage of time when you (as a smaller boat) can't count on that. And even if they are actively looking out, small boats are just... hard to see. Almost all of the deaths in sailing come from a small boat's crew falling asleep without appropriate watch (you're meant to fully scan the horizon at least every 20 minutes) and getting run down by a big boat.
This is a long way of saying that big boats are already mostly automated, and I think everyone will be safer if we go all the way on it, along with more robust sensors, instead of just pretending that there's always someone doing a perfect lookout.
Radar reflectors are generally legally required on sailboats where it would matter. Offshore most sailboats are outfitted with AIS transceivers and it's legally required in many places for commercial ships.
When not in a port, large ships will often adjust their course slightly to avoid coming too close to a small sailboat even if they're in a shipping channel (if there's reasonable space to do so). With AIS the ship can see exactly where the sailboat is, its heading, and its speed, so it's pretty easy to avoid it. They'll do the same based on radar data if that's all they have. It's common for both boats will tweak their course slightly. Personally, if it's possible, I usually try to adjust my course early enough to avoid a large ship having to react.
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Sailing vessels only get right of way with small vessels. You can't sail your little 20 ft trailer sailer in front of a container ship and expect them to give way.
I can't remember what the actual rule is, but I think it's somewhere around the 250 t mark that sailing boats no longer have right of way.
Of course you can’t expect a tanker to break/turn on a dime, but there’s nothing in the rules about tonnage.