Recognize what makes this moment difficult
Acknowledge the event directly without turning it into a lesson, comparison, prediction, or silver lining. For a message about how to apologize for forgetting to thank someone, use this factual base: name the exact action, the inconvenience it caused, and what you understand now.
Offer support that can be accepted
Offer one specific form of practical or emotional support and make clear that no immediate reply is needed. Offer the smallest useful repair and give a realistic time for completing it. Make the immediate next step clear enough that the recipient can answer without reconstructing the entire history.
Follow their pace rather than yours
Do not inflate the apology, fish for reassurance, or demand immediate forgiveness. If the person has asked for no contact, repair what you can without sending another message. The recipient decides whether they want conversation, ordinary company, practical help, professional support, or quiet.