How can I recover accidentally deleted Logic Pro X project files on MacBook Pro 2020 M1 without expensive software?

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

Restore the data from your Time Machine Backup. If you don't have a backup, your data is not retrievable.

<< unless I use some expensive data recovery software like Disk Drill. >>

...which REQUIRES that data to reside on a Rotating Magnetic drive, or your results will be NONE.

The drives in modern Macs are SSD drives, and when you say 'empty Trash', its gone forever.

Um, you have to start NOW.

Or when you need it, you will be in this exact position again.