When to use it
Use it when you're replying later than you'd like and the delay didn't cause real harm. Thanking someone for their patience acknowledges the wait and moves straight to what they need. If the delay did cause a problem, own it briefly first, then give the update.
Example
Client: “Any news on the proposal?”
You: “Thanks for your patience. Here's the update: the revised proposal is attached, with the pricing changes you asked for.”
In an email or Slack message
As an email opener: “Thanks for your patience on this. Here's where things stand:” followed by the answer. Save “I apologize” for a missed commitment, where it's warranted.