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mysql
An async MySQL client for PHP, optimizing database interactions with efficient non-blocking capabilities. Perfect for responsive, high-performance applications. (by amphp)
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InfluxDB
Power Real-Time Data Analytics at Scale. Get real-time insights from all types of time series data with InfluxDB. Ingest, query, and analyze billions of data points in real-time with unbounded cardinality.
While async DB exists, I don't think it is very important. Usually queries take just few milliseconds if DB is properly designed and has aggregate columns.
NOTE:
The number of mentions on this list indicates mentions on common posts plus user suggested alternatives.
Hence, a higher number means a more popular project.