Hey Fretnicker, I began experiencing these issues last week and toggling from 'Push' to 'Manual' for the gmail accounts on my iPhone (settings > mail > accounts > fetch new data) solved my issues instantly.
I hope this works for you too. Good luck!
Full post:
I use multiple gmail accounts on the Mail app/prog -- on both my iPhone & MacBook. Typically, I have no issues with syncing changes made in either direction and was being thrown when the changes I made on my iPhone (deleting, opening, moving to folders, etc.) were not syncing with my MacBook.
I opened webmail (mail.google.com, in this case) and found that the changes hadn't been made there either.
While other threads/solutions may be helpful for others (making sure iOS is up to date, phone restarted, fetched new data / synchronized accts on each device, toggled from deleted to archived in advanced settings), I was nearly to the point of deleting & adding the accounts back ... nearly, but didn't want to go through the hassle.
I'm sure glad I found this thread. Toggling from 'Push' to 'Manual' for the gmail accounts on my iPhone (settings > mail > accounts > fetch new data) worked immediately. Changes made on the iPhone synced with webmail and the Mail program on the MacBook in under a minute.