SQL Server Standard Edition - Limitation
As has been exhaustively commented, licensing questions are out of scope, however for technical clarification...
AlwaysOn is built on top of Failover Clusters, but is distinct from Failover Cluster Instances (FCI).  The difference mostly comes up with whether they share storage or not.
This link https://straightpathsql.com/archives/2019/02/basic-availability-groups-myths-truths/ does a good job of dispelling / clarifying basic availability groups.
YES, basic AG only allow a single database.  HOWEVER, you can have many, many availability groups with a database each.  This does complicate things a bit as it means that the databases won't necessarily move in sync with each other.  But you get what you get.
Given your scenario, I don't think managing one AG per database would be terribly problematic.  You are going to have to script your failover commands but checking AG health through TSQL should let you keep an eye on the herd (flock?  gaggle?) of AG's.  I wouldn't stress about it.
As for using Failover Cluster Instances instead of AG's, go for it.  They have no limitation and if you just want HA then it's easier to manage as you don't need to sync logins, jobs, etc.  It does mean that you must rely on your storage layer's HA rather than potentially having completely separate HA, but using FCI will allow you to do rolling upgrades and survive compute (CPU, memory, O/S) failure.