Can you tell me what the problem might be? Initially, everything worked well, but recently messages to email clients arrive with a long delay, while messages go to the hosting mail immediately.
Cloudflare does not handle emails in the first place. So whatever delay you are experiencing is something you need to clarify with your mail host I am afraid.
but the connections go through your network
They can’t, as - as I already said - Cloudflare does not handle email.
If you connected to a proxied record you couldn’t send emails at all but you are only getting delays you said.
Which hostname are you connecting to?
That is not a Cloudflare address, hence - as I said - you need to talk to your mail host.
After changing your DNS to DNS hosting the problems are over
Did you read what I wrote? Cloudflare does not handle emails, so the issue cannot be Cloudflare related.
If you had proxied records you wouldn’t be able to send emails at all, not just delays.
You might want to check out Email Troubleshooting