Short answer
No. Aktar has no servers. Files go straight from your Mac to the storage endpoint you configure, and your access keys are stored in the macOS Keychain.
There is no account system, analytics or telemetry. Aktar only talks to your storage endpoint (to upload, delete and test) and to your own public URL (to show previews and check that links work).
Aktar runs in the App Sandbox with the Hardened Runtime and is notarized by Apple. It only reads files you choose, drop or copy. The code is open source, so all of this can be verified on GitHub.