MacBook Pro keeps checking for MacOS updates continuously in a loop!

The additional information is important because the problem is not limited to macOS 27 failing to appear in Software Update. Software Update remains stuck on “Checking for updates,” softwareupdate --list-full-installers remains stuck on “Finding available software,” Safe Mode does not successfully start, and reinstalling macOS Tahoe 26.6 remains stuck at “4 hours 1 minute” for several hours. 

Because these failures occur through different mechanisms, I would stop repeating the same update attempts for now.

Before proceeding, I would also determine whether the Mac is enrolled in an MDM such as Jamf Pro. MDM can manage macOS software updates, including deferrals, target macOS versions, and other update restrictions. Therefore, an MDM configuration could potentially explain why macOS 27 is not being offered or why its installation is being managed differently. However, MDM would not necessarily explain all of the other symptoms, particularly the failure to enter Safe Mode or the stalled macOS reinstallation. Apple documents software-update management through MDM, and Jamf documents controls for deferring and managing macOS updates. (Apple, Jamf)

If the Mac is managed by Jamf, the appropriate next step is to have the Jamf administrator verify whether any software-update deferral, target-version, enforcement, or restriction policy applies to this Mac. I would not remove the MDM profile merely as a troubleshooting experiment. If the administrator confirms that no applicable policy is preventing the update, the investigation can proceed independently of MDM.

The next step should then be macOS Recovery rather than another attempt through Software Update or Safe Mode. Apple recommends using macOS Recovery when macOS installation through Software Update is unsuccessful. From Recovery, open Disk Utility and run First Aid on the startup volume/container as appropriate. This can determine whether the startup disk reports a filesystem or volume problem before attempting another installation. (Apple)

If First Aid completes without reporting a problem, restart into Recovery and choose Reinstall macOS. This provides a separate installation environment rather than attempting another installation from the running system. Reinstalling macOS from Recovery normally does not require erasing the startup disk, so the disk should not be erased unless a later step specifically calls for it and a current backup is available. (Apple)

The failure to reach Safe Mode is also relevant, but I would not make Safe Mode a prerequisite for continuing. If the correct Apple-silicon Safe Mode procedure has already been followed and the Mac still does not enter Safe Mode, Recovery provides another environment in which to investigate the problem. (Apple)

I also would not continue waiting indefinitely at “4 hours 1 minute remaining.” An installation estimate that remains unchanged for several hours, particularly alongside the other installation failures, should be treated as an unsuccessful installation attempt rather than simply being allowed to run indefinitely.

If Recovery works but First Aid reports a problem, or if a Recovery-based macOS reinstallation also fails, the exact error message becomes important. On Macs with Apple silicon or the T2 Security Chip, Apple documents a firmware Revive or Restore procedure for certain situations in which macOS installation or startup problems cannot otherwise be resolved. A Revive is generally considered before a Restore because it is designed to address firmware-related problems without erasing the Mac. (Apple)

Your " MacBook Pro (14 inches, 2021, M1 Pro chip, 16 GB memory) " is compatible with macOS 27.

Apple lists the MacBook Pro (14 inches, 2021, M1 Pro chip as compatible with macOS 27 Golden Gate, so compatibility is not the reason this model is excluded. (Apple Support)

Apple states that Software Update displays updates that are compatible with the particular Mac.

Because your MacBook Pro (14 inches, 2021, running macOS 26.6 but is not being offered macOS 27, the next useful step is to determine whether macOS 27 is actually being offered to that Mac through Apple's software-update service.

Open System Settings > General > Software Update and allow it to check for updates. Apple identifies this as the normal method for upgrading to macOS 27. (Apple Support)

If macOS 27 still does not appear, Apple provides a Terminal method for checking which full macOS installers are currently available for your particular Mac. Open Terminal and enter:

softwareupdate --list-full-installers

Apple states that this command displays the macOS versions currently available for the Mac. This is a useful diagnostic because it will establish whether macOS 27 is being offered to the M1 independently of the Software Update preference pane. (Apple Support)

If macOS 27 appears in that list, the full installer can then be downloaded using Apple's Terminal command softwareupdate --fetch-full-installer --full-installer-version 27.0

If macOS 27 does not appear, that result would provide useful information about why Software Update is not currently offering it.

Few more points related to this:

1. I tried the usual method to see the update (MacOS 27) like this: System Settings > General > Software Update. It keeps checking for hours together (with very good internet speed) and doesn't come out of that loop.
2. I tried the terminal method also (softwareupdate --list-full-installers). But there also "Finding available software" is displayed for hours without any yield!
3. I even tried to reinstall the macOS Tahoe 26.6, by trying to install it through Safe Mode. The OS looks like it is trying to boot/load for Safe Mode but fails to display the Safe Mode (followed the procedure to boot in Safe Mode). Several attempts were made to boot the OS in Safe Mode, but failed to boot in Safe Mode.
4. I tried to Reinstall MacOS Tahoe 26.6. Inspite of stable and high speed internet, it gets stuck at "4 hours 1 minute" remaining forever (it was kept for several hours together!) and that also fails. I thought of installing the new Tahoe 26.6 (with possible rectification for any bugs/errors in the current OS) and then try for MacOs 27. That is also failing!