Based on Microsoft's documentation the SLA for storage account is defined as,
We guarantee that at least 99.9% (99% for Cool Access Tier) of the time, we will successfully process requests to write data to Locally Redundant Storage (LRS), Zone Redundant Storage (ZRS), and Geo Redundant Storage (GRS) Accounts and Read Access-Geo Redundant Storage (RA-GRS) Accounts
Similarly looking at Azure Storage Redundancy section, for ZRS
ZRS offers durability for Azure Storage data objects of at least 99.9999999999% (12 9's) over a given year. With ZRS, your data is still accessible for both read and write operations even if a zone becomes unavailable
Am I correct in assuming that the Storage account(with ZRS) is available(R/W) 12 9's over the period of a year and not 3 9's?
The percentage in the SLA doc is referring to Availability(it means that system is up, data can be accessed), and in ZRS doc is referring to Durability(it means that no data is lost or corruption when failure occurs).
The read/write operation depends on the Availability. So for Storage account(with ZRS), it is 3 9's. You can also refer to this table for more details.