The application should have logic to re-try connections. When you scale, there is a brief moment ~30-45seconds when the app wont be able to connect to the database and then resumes if you re-try connection.
/I work at Microsoft on the managed PostgreSQL service/
Compute units are a measure of computing throughput for your instance with pre-configured amount of RAM. We do not count hyperthreads as core. So 100 compute units is 1 core, 200 compute units is 2 cores, etc.
/works at Microsoft and managed PostgreSQL service /
You can scale by clicking on the Pricing tier. However note that scaling operations currently only support within a service tier. i.e, scaling up/down within Basic and scaling up/down within standard. Ability to scale across service tiers will come soon. /works at Microsoft and the managed PostgreSQL service /