Emails being deleted in Gmail folders

I have a iPhone 14 pro, with OS 16.03. I feed my gmail account through thhe apple email system. I got a notice that I was running out of icloud space and found that I had never truly deleted my read/unsaved emails in gmail. Following instructions in the apple support community , I started to delete the old emails that were put in "archives", one at a time. I then had to research an email that I saed in a folder , created within my apple email system and when I opened to folder up, all the saved eamils were deleted. I went to my gmail app on my macbook air and was able to find the deleted emails and was asked if I wanted to restore my emails. I went through the 45 emails and got them restored burt as new emails. Now I can't move then back int the folders and when I tested a few unimportant folders, the emails are wiped out.