The Talos Principle – QR Codes Visible That Shouldn’t Be

According to this walkthrough:

These small items allow you to make your mark on the world by painting your own QR code on the walls. The messages you leave can be seen by any other player that is on your friends list, so make things interesting by hiding them in obscure areas. Of note, the paint bucket is the only item in the world that can pass through the purple puzzle gates.

So its purpose is to leave messages around for your friends to find.

There are also 2 achievements related to paint buckets:

• Leave Your Mark: Unlocked after using a paint bucket to write a QR message for the first time.

• Split Personality: Find the paintbuck in a level that has a recorder puzzle. Bring the paintbucket into the puzzle and start the recording. During this time, paint a QR code and then stop the recording. During playback, read the ghost QR code to obtain the achievement.

I almost completed the game and now I have quite good estimation of number of puzzle it has. There are:

1. Exactly 99 sigils puzzles: 18 green + 23 yellow + 49 red + 9 grey.
2. At least 30 star puzzles (some of them are not really puzzles, but exploration tasks). May be more, but I don't thinks so, since exactly 30 stars are needed for 3 doors and currently I know exactly 30 stars locations.
3. Exactly 6 puzzles at the tower.
4. Exactly 3 messengers puzzles. But those are extremely simple.
5. At least 39 easter eggs, these usually also don't require a puzzle solving, but exploration.

In total this would be 138 puzzles + 39 eggs, may be few more eggs.

P.S. New DLC: "Road to Gehenna" additionally provides 24 very good sigil-like puzzles + 16 star-like puzzles + several eggs.