Backup and Restore Oracle database in Azure
As far as I know, Oracle databases in Azure are not provided as DBaaS, you get OS access, so it does not really affect the choice.

RMAN is efficient when working with large databases, while Data Pump is trouble-free and is easier to manage for someone not familiar with DBA tasks. A 260 GB database is not big, I would just export-import the database.

To restore an RMAN backup, you need the same platform + the same or higher software version. If your software version is higher, you need to immediately upgrade the database after restoring it.

With Data Pump you can just import the data directly to a higher version database, even on a different platform. Loading data with Data Pump is usually fast. The slow parts are creating indexes and validating constraints. This is a one-time operation, it should not affect performance in a negative way. In fact, it reorganizes tables and indexes, it may even improve the performance depending on their current state.