Recovering document that has been sent to the bin from 'File Share'

It’s my experience that when deleting a file from a shared folder, the OS warns me that the deletion will be immediate -and I assume- irreversible.

The only way to recover that file will be from a backup.

Is the file backed up?

If you do not have a recent local, disk-based backup, your computer is like a ticking Time bomb. You are only one disk failure, one crazy software, or one "oops" away from losing EVERYTHING! Drives do not last forever. It is not a question of IF it will fail, only WHEN it will fail. In addition, you never know when crazy software or Pilot Error throws away far more than you intended.

If you are using another direct-to-disk backup method that you prefer, and you currently have a recent disk-based backup, that is great. If not, you should consider using Built-in Time Machine. Take steps to acquire an external drive as soon as possible. If you buy one, a drive 2 to 3 times or larger than your boot drive is preferable for long term trouble-free operation. Do not pay extra for a drive that is fast.  (You can get by for a while with a "found" smaller drive if necessary, but it will eventually become annoying).

Attach your external drive and use

Settings > General > Time machine ...

... to turn on Time Machine and specify what drive to store your Backups on.  It may ask to initialize the new drive, and that is as expected. APFS format is default format if running MacOS 11 Big Sur or later.

Time machine works quietly and automatically in the background, without interrupting your regular work, and only saves the incremental changes (after the first full backup). Time machine backs up your machine — including every connected drive that is in a Mac compatible format. it can not back up Windows format drives.

Time Machine's "claim to fame" is that it is the backup that gets done. It does not ruin performance of the rest of the computer while doing its backup operations. You do not have to set aside a "Special Time" when you only do backups. When you need it, your Time machine Backup is much more likely to be there.

How to use Time Machine to Backup or Restore your Mac:

Back up your Mac with Time Machine - Apple Support

Time Machine may spend all afternoon making your first full backup. You can continue to do your regular work while it does this. The first Full Backup is by far the biggest backup.

Yes PLEASE use Time Machine and a good quality External Hard Disk.3

'Trashing' local files on your Mac does not copy them to a place named Trash. Rather, it sets the 'in The Trash' bit on the file where it sits, and adds that file name to a linked list of [local] Trash-can contents for that specific drive.

When manipulating files that are still on a Shared Volume of any sort, they can not be marked as "in the Trash", because the Sharing protocols do not support that concept. Since Server files may also have multiple Readers (others who may be able to read that file), D.I. Johnson is correct in that they can only be deleted immediately.

If you had COPIED that remote file to your Mac, rather than just 'access it in place' on the File Server, this whole process would be done using local file rules, and the file copy would still be in your local Trash, and could be selected and "put away" using Finder commands.

Yes! I agree with user @rkaufmann87 100%.

Back up your Mac with Time Machine - Apple Support

For safety concern, you can back up via the time machine, on external drive or cloud drive.