No, certain features of Elasticsearch require a commercial license. See Subscriptions | Elastic Stack Products & Support | Elastic and FAQ on Software Licensing | Elastic for more information.
The AGPL only applies to (most but not all of) the source code, not to the binary distributions like the 8.15.3 release tarball you downloaded. Also, the license changes only apply from 8.16.0 onwards.
If you currently have some data in a basic-licensed cluster and you build an AGPL-only version yourself then I expect the AGPL-only version will be able to read the same data. Not tried that tho.
That said, the Elastic license (text, FAQ) is very permissive, are you sure you need to build your own AGPL-only distribution?