Greetings!
There will be a small downtime would be expected during scaling operation, When you expand the vcore on sql database, it will have small downtime usually several seconds to 1 min. expected processing time is at longest 1 min/ 1 GB for Business critical, but probably it will not take that long (1 min / 1 GB is just longest scenario as noted in doc). it will have small downtime and drop any connections during downtime
When you expand only disk size on sql database, there is no downtime expected if it is within the same service level (within BC or within GP, because there is no disk change, just expand), however we can not guarantee that there is no downtime (technically it will no downtime), so I would say, mostly there is no downtime.
Scale single database resources - Azure SQL Database | Microsoft Learn
expected time latency till complete scaling with below docs.
Regards
Geetha