Per definition, highly available means no interruption of service. Failover does not meet this criterion since there is an interruption.

I've never seen it defined that way, neither in industry material nor academia, so I guess "citation needed"?

These things always have limits, and what's defined as "availability" and acceptable failure rates/times is application-dependent. High-availability merely describes reaching a goal that's higher than a "conventional" setup can achieve, and failover is a fairly obvious way of massively reducing Time-To-Recovery