I don't think that's the issue here.

The sunk costs fallacy would be relevant if people were swayed by the money they already spent, rather than by the cost of switching. It's easy to disentangle the two. In the case of apartments, one is your past rent payments, the other is your moving costs.

My impression is that people often say "it's too expensive and troublesome to move and too hard to break the lease" and don't often say "I already spent a lot of money on the lease".

Transaction costs are real, and there's nothing irrational about considering them.