Hi Saraswathan
If your Windows 11 was activated digitally (linked to your Microsoft account) rather than with a physical product key, removing the device from your account's device list doesn't delete the license itself — it's still tied to that PC's hardware, so once you get it back from repair it should reactivate automatically as long as the motherboard wasn't replaced. If it was a motherboard repair, that's actually the more common cause of activation issues than the device list removal.
To actually retrieve the key/license info before or after repair, here are your options:
If you still have access to the PC, open Command Prompt as admin and run slmgr /dli for basic license info, or wmic path softwarelicensingservice get OA3xOriginalProductKey to pull the OEM key embedded in the BIOS/firmware (works for pre-installed Windows).
If the PC is already gone for repair and you can't run commands on it, check whether you bought Windows separately — the key would be in the confirmation email from Microsoft or the retailer, or on the sticker/card if it was a physical purchase.
Once you get the machine back, just sign back into your Microsoft account and go to Settings > System > Activation to add the device back — it should pick up the digital license automatically. If it doesn't reactivate on its own after that, come back and mention whether the motherboard was replaced, since that changes the fix.