Auto Save? Where are you?

When editing in Design View or Live View, hit Refresh (F5) to refresh the screen. 

In browser preview, you must commit changes by saving the file and then refresh (F5) your browser.

Unlike VS Code, Dreamweaver is also a site manager. 

DW saves files and manages asset paths to your local site folder (assuming you defined one before you began your project).   Site > New Site >  SiteName > location: C:\yourSiteFolder\

Use Ctrl / Cmd + S often during development to protect data. Automatic File Recovery works if DW crashes due to power failure, etc....  It automatically recovers your file but only if you saved it beforehand.

Hope that helps.

Nope, you're not missing anything DW deosn't have that functionality and, given it's current "Minimum Development" status, it's not likely to ever get it.

As it stands, Adobe is keeping the program on life support for the current customer base. No new features or bug fixes are planned going forward aside from security patches, OS compatibility patches, and third party library updates.