I've ran into an integer PK being almost exhausted in values twice now. In one of these cases I used pg-osc to rewrite a 8TB table on disk without downtime over a period of a week to fix the issue. In the other case it was about 6TB within 2 days. Its doable, but the amount of planning and time it takes is non-trivial.
I so far have no found any other viable solutions either. I keep hearing about logical replication but I haven't seen a great real-world solution at scale so far.