I have shared this issue in other threads and wanted to share here for the sake of OP and others: I can confirm the same issue after upgrading to 4.8. Emails are sending fine, but the progress animation continues to spin for all forms with no confirmation/success message displayed.
I figured this might be related to the change to REST API. We had REST API disabled due to previous security concerns. Turned it back on after disabling and clearing all local and server caches, still had issues with 4.8.
After a bunch of testing, nothing helpful popped up in console or in error logs, so have reverted to version 4.7 of CF7. Back to working fine. I’m not sure what’s going on there but it seems to be related to changes in the plugin between these versions.
If anyone needs a quick way to rollback, I recommend this plugin: https://www.ads-software.com/plugins/wp-rollback/