Check for Updates on MacBook Air will not complete

If macOS 26.7.1 does not appear in Software Update, try the following steps in order.

1. If you are using a VPN, shut it off.
2. Restart your Mac.
3. Go to System Settings > General > Software Update and check again. Press Command-R to refresh that settings pane, just in case.

If macOS 26.7.1 still does not appear, you can check which software updates are currently being offered to your Mac.

Open Terminal (find the app with Spotlight or in Applications > Utilities) and paste the following, then press return:

softwareupdate --list-full-installers

If macOS 26.7.1 appears in that list, you can download the full installer with:

softwareupdate --fetch-full-installer --full-installer-version 26.7.1

If you are not offered an update in System Settings and/or are unable to install an update downloaded via Terminal, then is likely that you are in Low data mode. Users have reported difficulty upgrading macOS over Wi-Fi in Low data mode, and that toggling that setting OFF enables them to perform a Software Update. 

Turn off Low data mode

• Open System Settings 
• Click on Wi-Fi
• Click on the Details button on the right side of your connected network
• Toggle the setting off

More info from Apple: Wi-Fi settings on Mac - Apple Support

Since your MacBook Air (M2, 2022) is already running macOS Tahoe 26.6, the issue is that Software Update keeps spinning and times out when checking for newer updates. This does not necessarily mean an update is available or that macOS needs to be reinstalled.

First, restart your Mac and try again under System Settings > General > Software Update.

Before further troubleshooting, check Apple System Status for any reported issues affecting macOS Software Update. If no relevant issue is reported, check that your internet connection is working normally, verify that the date and time are correct, and temporarily disconnect any VPN or third-party network security software. If possible, try another Wi-Fi network.

You can also use Terminal to check whether macOS can retrieve available updates. Open Applications > Utilities > Terminal, enter the following command, and press Return:

softwareupdate --list

This checks for available software updates without installing them. Interpret the results as follows:

• An update is listed: Terminal retrieved information about available updates. Note the names and versions and compare them with what appears in System Settings.

• No new software available. The command did not find any applicable updates at that time. This does not prove that the Mac is fully up to date or that the Software Update problem is resolved.

• The command hangs or does not finish: The command-line check is also failing to complete. This does not, by itself, establish the cause.

• An error appears: Record the exact message, as it may help identify the problem.

To check which full macOS installers are available, you can also run:

softwareupdate --list-full-installers

This lists available full macOS installers, not routine software updates. It does not install anything. If no installers are listed, that does not necessarily indicate a problem with ordinary software updates.

If the problem persists, try checking Software Update in Safe Mode. 

Shut down your Mac, press and hold the power button until startup options appear, select your startup disk, hold Shift, and click Continue in Safe Mode. Then try checking for updates again.

If Software Update and Terminal both fail to complete, or Terminal reports an error, note the exact output and contact Apple Support for further diagnosis. I would not reinstall macOS or erase the Mac as an initial troubleshooting step.

Apple references: Update macOS on Mac and How to download and install macOS.

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Bottom line: patience is a virtue.