Do timeline resolution changes lower clip quality?

Before importing anything in to my project, I made my timeline resolution 1080p and my project FPS 60. While editing, I was getting some playback lag, so I changed my timeline resolution to 720p(not knowing that I can just change the playback resolution). Before exporting, I changed my timeline resolution back to 1080p and made sure that was what I was exporting it as in the deliver panel. Looking at the video, it seems like it’s lower quality than it should be. Am I wrong or did that change affect it? And if so, is there anything I can do to fix the issue?

Another question I had: Would a change to my playback resolution make my project less laggy for future projects?

[Peter Chamberlain]

The timeline resolution is the correct way to change for faster performance and back up to your source or output res for rendering,

If you are concerned about quality, render to dpx files or a low compression format and check

Am I wrong or did that change affect it?

You can check this way: take 4K source and put it into the say 960X540, then before rendering in properties of project change TL resolution back to 4K. Render to 4K. I´m sure there won´t be any change in quality.

Half resolution or quarter resolution options are also made for this btw...