Does "into" mean "in the middle of" or "until the middle of" there, or something else? [closed]

I've come across a couple of sentences containing the word "into" before "time"-words, but couldn't have found "time"-meanings for "into" in dictionaries. So could you explain what "into" mean in the following contexts.

The teams worked into the night and continue to make progress. enter link description here

He advised the EU capitals he would announce on Wednesday whether negotiations on an agreement would have to continue into next week. enter link description here

Imagine a random shape. now imagine a mark anywhere in that shape. You can place anything you want "into" that position in the shape.

Into does not mean middle it just means in, it could mean second or second to last, right at the top or at the very bottom.

The teams worked into the night and continue to make progress

Imagine a day split in half with 2 blocks a day block and a night block. "into the night" means at any point in the night block, so say night starts at 7pm (for work purposes) into the night means any point after 7pm and before 7am.

If you worked the night shift and

The teams worked into the day and continue to make progress

would mean working any point after 7am when the night shift ended.

He advised the EU capitals he would announce on Wednesday whether negotiations on an agreement would have to continue into next week

This means that the negotiations would be continuing past the block of time that is this week and continue until some point after Sunday.