Hi Maciej,
You did the right thing checking slmgr, but the banner in Settings is not the authority for ESU. On Windows 10, devices licensed through ESU can keep showing the end-of-support message even when they are eligible and will receive ESU updates. Microsoft's verification method is different from that banner.
The quickest way to confirm ESU on any one machine is to check two things.
First, open Event Viewer and browse to Applications and Services Logs > Microsoft > Windows > ClipESU > Operational. Look for Event ID 113 that says the W365 ESU license was successfully installed. That event is Microsoft's signal that the ESU license is in place.
Second, check the ESU eligibility flag in the registry. From an elevated PowerShell window run:
(Get-ItemProperty -Path 'HKLM:\SOFTWARE\Microsoft\Windows NT\CurrentVersion\SoftwareProtectionPlatform\ESU').Win10CommercialW365ESUEligible
A value of 1 means the device is enrolled and eligible to receive ESU updates. This key and value are the documented check.
If you see Event 113 and that registry value is 1, you can ignore the Settings banner. The device will pick up the monthly ESU security CUs when Microsoft releases them. Microsoft's ESU pages describe the program and its scope, but they point admins to the ClipESU event and that registry value for confirmation rather than the Settings UI.
If either check is missing on any PC, tell me which one and we will fix that point next.