If it's an extension, you can apply for it until the last day of your current stamp with no problem.
But, You better get the latest requirements list for a 1-year extension in advance as you won't have many days left when you apply for it. It might take days if some additional documents are required.
This is the reason why we always tell members to get the latest requirements list from your local immigration office. Always there is possibility of detailed requirements changes.
Yes, you will be overstay if you stay longer than your current entry stamp, even for 1 day. What let you stay inside Thailand legally is entry or permit-to-stay stamp, not the visa itself.
You do nothing for just moving out from Thailand regarding immigration matters. No notification, anything.
Just unnecessary additional: You can get a re-entry permit if you thing you will visit Thailand again before May 2025 to keep your current stamp alive. If no plan to travel soon, no need to get it either.
, you have to wait at least 2 weeks depending the office. Bangkok, Phuket, a few more accept tourism extension when your stamp remaining 45 days or less. Most when less than 30 days. But Pattaya, Samui, and a few others accept tourism extension application only in the last week of your stamp.