need help with restoring my macbook air 256GB from macbook pro 1TB

If you had a spare external drive with 1 TB or more of capacity, I wonder if you could format that drive as an APFS drive, then restore your Time Machine backup to it to create an external startup drive.

Restore new external hard drive from Time… - Apple Community

If you're talking about the user-level Library folder, note that the Finder normally hides that unless you have your view options (View > Show View Options) for your home directory set to show that Library folder. (The setting only appears in the dialog when you have a home directory selected, so it's easy not to realize that the option is there.)

Leaving aside the issue of why anyone with a computer having >500 GB of data on it would buy a new computer with less than half of that amount of storage, with the drive connected try going to System Settings > General > Time Machine, clicking the (+) button at the bottom of the (likely empty) list and selecting the drive. If prompted to Claim Existing Backups select that option, and then you should be able to browse the backups using the TM browser.

A red x? or the 'do not enter' sign (white – in a red circle)? The latter is a permissions issue, can be adjusted in Get Info.