Yes, it's incompatible, although you might be fine if you aren't distributing it or running it as a service. SSPL requires re-licensing of all code to the SSPL, GPL has provisions that disallow re-licensing.
> the simple requirement that if you provide the product as a service, you must also publicly release any modifications as well as the source code of your management layers under SSPL
This provision is effectively impossible for anyone to comply with in practice. Calling this a "simple requirement" is a barefaced lie.
Especially that no independent party with any authority (ie. a court) determined what's covered under "management layers". If I use a custom kernel (that's optimized to run the JVM and has filesystem and block storage optimizations for ES), do I have to provide the source for that? (It seems trivial that it's not "management", but naturally Elastic's interest lies in arguing that yes, that are covered under management layers too.)
> the simple requirement that if you provide the product as a service, you must also publicly release any modifications as well as the source code of your management layers under SSPL
This provision is effectively impossible for anyone to comply with in practice. Calling this a "simple requirement" is a barefaced lie.