Linking Gmail email dates to google sheets?

Is there a specific way I can link my google sheets to the dates of my emails (gmail) to specific emails?

I work for a company that deals with payments sometimes so a sheet would look like

1. Name: John Smith
2. Email: johnsmith123@email.com
3. Date of first reminder (this would be automatic)
4. Date of second reminder (also automatic)

Is there a way for me to link the sheets so that when I send an email to (ex) johnsmith123@email.com, Google Sheets tracks the date of my first email to him, then the date of my second email to him?He would be marked as "lost" or "permanently unresponsive" manually in another column if he does not reply after two emails, and that would take him off of the list of people being tracked automatically.

Any and all help is appreciated.