Keep Zoho Mail and add PostPike

Zoho calls it Split Delivery.

Pass unknown addresses on

Sign in to the Zoho Mail Admin console, and select Mail Settings, then Email Routing, in the left pane.
Select Configure routing or Add, and choose your domain.
For Destination Host, enter mx1.postpike.net.
For Verification Email Address, enter one of your PostPike mailboxes on this domain. Zoho sends it a message: open it in webmail, or ask your AI agent to read it, and confirm.
Select Add. Once it's verified, select the routing in the list and turn on Status under Routing Details.
Select Basic settings and choose Split Delivery, which delivers mail for addresses that don't exist in Zoho to the destination host.

Then select Test on your domain's page. If the test doesn't arrive, check that the routing's status is on and that Zoho has no catch-all address for the domain.

From Zoho Mail: Email Routing. Menus change: if something here doesn't match what you see, tell us.