What does “recommended for approval” on the AOS mean?

That sounds like things are moving in the right direction! USCIS is slow. Very slow at times. If 30 days pass, submit an inquiry.

It means that they will approve your green card. You should receive a formal approval notice in 30 days.

It is common that the online case status do not follow in lockstep with the mailed notices. It is not unusual that written notices are mailed out before a case is updated for online viewing and in particular, a time interval of three weeks between online update and mailed notices is not unusual. In essence, the online status will soon be available for viewing to complement the mailed notice.

"Recommended for approval" usually means that the adjudicator has completed his or review of the application and is waiting for supervisor concurrence, background security check, or other clearance in order to proceed with the final approval. If you do not receive your welcome notice (I-485 approval notice) within 60 days, you should call the USCIS customer service number (1-800-375-5283) or have your attorney inquire for you, in order to open a service request on the status of your application.

There should be no need for worry at this time. The next step would be for the U.S. consulate in your country to contact you for a visa interview.

"Recommended for approval" means just that; apparently they have not updated the system to show that your application for adjustment of status on Form I-485 has been approved, which would be necessary for you to become a conditional permanent resident in the United States. Without knowing more, I would not have any reason to believe that USCIS would change their decision. You should wait a reasonable period of time and if that does not work, you can make an inquiry to determine the status of your I-485 application.

I would say you should buy some champagne and put it on ice. If you are Chinese, there may be a quota issue, but if not, my guess is you are likely to get an approval in the mail soon.

Most likely the permanent resident card will come next; keep monitoring the case status.

A reentry permit will most likely be granted up to the period of validity of the extension granted while the I-829 is pending. It is unlikely that a reentry permit will be granted for the full two year period a reentry permit is generally valid.