There is no manual approval process for Spotify submission. The submission process is immediate: once the switch is green, your feed has been sent to Spotify. Spotify usually takes only a few minutes for new podcasts to be listed. Existing shows with more content can take longer to process. Almost all podcasts are listed within an hour of submission.
If your podcast has not appeared on Spotify after 24 hours, please get in touch with Pinecast support so we can investigate further.