Short answer
Click Test Connection when adding or editing a destination. Aktar checks that the bucket exists, that it can write to it, and whether files are reachable through your Public Base URL.
Behind the scenes it uploads a tiny text file named _aktar_test_….txt, requests it through your Public Base URL, then deletes it again.
The result tells you what to fix: a bucket that can't be found, rejected credentials, keys without write permission, or a public URL that doesn't serve files (see Access Denied errors).