I need to re-install MS 365 on one of my two laptops following a complete disk reformat etc. When I log in from my back-up laptop, my MS 365 subscription is listed (renews March 2024) but if I log in from the laptop on which I want to re-install, there is no such subscription reflected. How can I proceed ? Thanks for assistance.

If you're sure you're using the right account, try updating Microsoft 365 on the laptop without the subscription. Sometimes, when you update the software, it can help fix the subscription issue and show that your subscription is active.

Quite some time ago, something similar happened to me with my MS 365 subscription. I basically go from the backup laptop, and voilà—there's my MS 365 subscription, clear as the day. But when I switch over to the laptop I want to reinstall, it's like my subscription vanished into thin air. From there, I went through all the regular troubleshooting steps. Checked my Microsoft account, double-checked the installation, but nope. Just not showing up on that laptop. In the end, I tried reinstalling MS 365 using the same Microsoft account credentials that I had for my backup laptop.
To keep your data safe, have you heard about Google Workspace Cloud Backup Europe? Might be worth considering, especially with all the digital chaos we deal with these days.