Update error code 30088-27 Office 2021 what to do to get corrected????

I don't know what the "online repair" is--which didn't work for you, you wrote? I did try to modify the installation, attempting a repair via that means, which was an utter failure, as it simply uninstalled Office, and if it was supposed to repair it, it didn't complete, apparently.

So apparently the rental version also is no longer updating?

So apparently the rental version also is no longer updating?

Correct. Read the posts in the thread.

FYI

If you go to the Windows Control Panel - Programs, you will find Microsoft Office in the list of installed programs.

Here you can choose to either do a quick fix, or an online fix. The online fix uses the internet. But it is not the sollution for this issue.

I see no need to try to revert to a previous build or check your network.

It looks like the update using c2r (Click to Run) is broken on certain but not all systems as of Office versions 2406.

Not the Office applications them self.

You could wait until it is reported to be fixed. Plenty people, including at Microsoft I presume, are now aware.

If there is an office update you need you can do an update using the elevated cmd prompt and update office, as explaned earlier in this thread.

You can check the latest versions using the Office history links mentioned earlier by Linn.L

Give Microsoft the time they need to fix this. Since it concerns some but not all systems this could be a little bit more complex.

If you like to get an idea, in the temp directory, depending on your pc settings, but standard in C:\Windows\temp

C2R writes a readable .log file every time you check for an update. If this goes wrong, you find a line reporting back the 30088 error.

Just received a message in the other thread I created before joining this one. It offers hope, if not a solution:

Maxine.C - MSFT has replied to your question Office Home and Business 2019 Retail will not update in Microsoft Support Community.

Dear mschmieg   

Thank you very much for sharing your feedback! As this issue was caused by an update, we are already actively working on it. Please be patient and wait for the next update when we will try our best to resolve this issue. Thank you again for your understanding and support! 

Best Regards,    

Maxine | Microsoft Community Support Specialist