The sewage/water company would only be responsible for looking after the drains if they were shared. Otherwise, they are just your responsibility to maintain.
Definitely agree with installing a root barrier. I've had to do this occasionally for concrete foundations near a boundary tree (or even some hedges.)
Probably a reinforced flexible barrier, the sort of thing used with invading Japanese knotwood.
Easy to install, but a bit of a game. A trench dug around 1500mm (5') deep, parallel to the drains/pavers.
Fit the barrier and backfill.
A TV camera down the drains would be a good idea. I've seen drains well filled with roots, where the only fix was to excavate and replace the drain run.