I would like to run a failover setup for my Access Server. Do I have to pay extra for a failover software license?

No, if you use a software subscription license you can use it on the primary and secondary node of the Access Server without extra charge.

It is recommended to purchase and activate a subscription activation key. It is designed with this use-case in mind. This type of software license activation key allows you to activate on multiple Access Servers at the same time. It also automatically migrates from one node to the other in a LAN model failover pair. This means that if you activate a subscription activation key on the currently active node in a failover pair, the other one will also automatically use it once a failover event occurs.