How to let users know that updates are not real time

When reading the question, the Amazon parcel tracking app sprang to mind. That shows the location of the driver, but only updates every 30 seconds or so. In between time, it shows how long ago it was updated, incrementing every 10 seconds.

Something similar might suit your needs - as it gives a view of how current your information is but still updates at a frequency that makes sense for your users.

There is no reason to calculate this for the user unless you truly believe they cannot tell time.

"Your order will be ready at 18:12" should suffice; it does not matter how many minutes away that is.

This allows the user to make a quick mental note of when to check on their order instead of forcing them to think "Oh, it's 18:10 right now and 9 minutes ago it said I have 23 minutes left; or was that 12 minutes ago? Screw it I guess I'll just open the app again." Your current plan gives the end-user both a memory problem and a math problem all at once; don't do that.

Add the time of the last update. That way users have a better understanding how old or new the information is. But it only works if you can use the users system clock to determine the shown time.

If you see that people don't think about refreshing the page, you can also provide a link for it:

Second choice is better to manage user expectations about estimated time.

You can create background process auto refresh every X second for update estimated time left, so user don't need to refresh the browser manually.

Make Optimistic UI with time display as countdown and give progress bar on circle.