How to model a supervised recommender system with varying data
In this task you're missing something: you don't have any features to represent a specific visitor.
This means that the best movie that your model can predict is the one which is selected the most often by any visitor. As a consequence, the only thing that the model can learn from such a dataset is to associate every possible sequence with the most frequently selected movie given this sequence. Of course it would have to generalize a bit for sequences which don't appear in the training data, but that's the most ML there is in this task. In theory the task can be done just by counting the joint frequency sequence+selected-movie in order to calculate the conditional probability selected-movie given sequence.

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The standard way to represent a set would be one hot encoding. It's doable even with 2000 features, assuming there are enough instances in the data. In this basic option you could certainly reduce the number of features by removing the movies which are never/rarely proposed or never/rarely selected. This would be unlikely to achieve performance, because if there are no or few cases where a movie is proposed/selected, then the model cannot use this information (or if it does it's going to cause overfitting).
I could think of a couple alternative approaches:

Apply clustering on the sequences of movies as OHE (without the target variable), then train a model with for every cluster: this way there are less features to deal with for every model.

Just rank all the movies by order of preference based on how often the movie is selected. Given that there is no user preference, it can be assumed that there is a total order on the movies:

the top preferred movie is always selected, whatever the other movies proposed

the 2nd top preferred movie is always selected, unless the first one is proposed as well

... the $n^{th}$ top is always selected, unless another one higher in the top is proposed as well


To predict the selected movie, just pick the highest ranked among the 3-5 proposed.