Based on your description, I would investigate this systematically before concluding that your MacBook Air M5 has a hardware problem or that macOS 26.6 contains a bug.
Your MacBook is located correctly while connected to Wi-Fi, but its location disappears completely when it goes offline. You have tested this in busy public places, with the MacBook powered on in your car or backpack, and have already confirmed that Find My Mac, Find My network, Location Services, and Bluetooth are enabled.
The most important question is whether this is a limitation of iCloud.com or a genuine problem with the MacBook's participation in the offline Find My network.
First, I would check Apple's documentation regarding offline finding. Apple distinguishes between Find Devices on iCloud.com and the Find My app. The website displays the last known location for up to 24 hours, whereas the Find My app can retain locations reported through the Find My network for up to seven days.
Locate a device in Find Devices on iCloud.com - Apple Support (CA)
This distinction is important because the absence of a location on iCloud.com does not necessarily prove that the offline Find My network is malfunctioning.
Next, I would verify that the MacBook is genuinely offline. Disconnect it from Wi-Fi and any other internet connection, including Ethernet or a hotspot, while keeping Bluetooth enabled. For the initial test, leave the MacBook powered on and awake. Check whether it remains listed in Find My but displays Offline or No location found.
The next step would be to test the MacBook using the Find My app rather than relying exclusively on iCloud.com. You do not need to own an iPhone for this. If possible, use a trusted person's Apple device, with their permission, to check whether the MacBook's offline location appears in Find My.
If the location appears in the Find My app but not on iCloud.com, this would suggest that the discrepancy is related to the website rather than the MacBook's participation in the network.
If the location is missing from both, I would proceed with further testing.
Although you have already checked the relevant settings, I would verify them again under System Settings > your Apple Account > iCloud > See All → Find My Mac. Confirm that both Find My Mac and Find My network are enabled.
Then check System Settings > Privacy & Security > Location Services. Make sure Location Services is enabled and that Find My has permission to access location information. Also check System Services for Find My Mac.
Apple's setup instructions are available here:
Set up Find My on Mac - Apple Support (CA)
I would then perform a controlled test. Connect the MacBook to Wi-Fi and confirm that Find My displays its correct location. Disconnect Wi-Fi, leave Bluetooth enabled, and take it to a busy public location. Keep it powered on and awake for approximately 15–30 minutes.
Afterward, reconnect it to Wi-Fi and check Find My again. Repeat this experiment in different locations.
Nearby Apple devices must be participating in the Find My network and successfully detect and relay the MacBook's Bluetooth signal. Therefore, even a busy public place does not guarantee that a location report will be received.
I would also repeat the test with the MacBook asleep and its lid closed. Find My is designed to locate offline Macs, including sleeping devices, but testing while awake first helps eliminate sleep-related variables.
If the MacBook never receives an offline location report, I would restart it and install any newer macOS update available under System Settings > General > Software Update.
If the problem persists, I would contact Apple Support and specifically ask whether they can investigate the MacBook's participation in the offline Find My network, rather than simply confirming that Find My Mac is enabled.
Contact - Official Apple Support
My conclusion is that I would not immediately assume the MacBook is defective. The fact that you use iCloud.com is particularly relevant because its offline-location behavior differs from that of the Find My app.
If the location is missing only from iCloud.com, this may be an expected limitation of the website. If it is also missing from the Find My app after repeated controlled tests, despite the correct configuration, then a macOS 26.6 issue or a problem with the MacBook's Find My network participation becomes a reasonable possibility.
The most useful next step is to test the MacBook's offline location using the Find My app on another Apple device. This should help distinguish a website limitation from a genuine problem with offline finding