To store Unique-Id you can use single-value extended property. Please refer to this example to create singleValueExtendedProperties.
Post creating singleValueExtendedProperties you can use filter to get only those events with your custom value.
Please refer to this sample request: https://graph.microsoft.com/v1.0/me/events?$filter=singleValueExtendedProperties/Any(ep: ep/id eq 'String {66f5a359-4659-4830-9070-0114*****} Name Custom_Property_Testing' and contains(ep/value, 'Think'))
If you want to expand singleValueExtendedProperties also while filtering please refer to the below sample screenshot.
Please refer to this documentation for more details.
Hope this helps.
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