Rethinking the Thief's Sneak/Hide Skills

I’ve been toying with reconfiguring the thief. As part of this exercise, I’ve been thinking about stealth and how we apply it and some other ways it could work. I’ve got an idea on subsuming hide and move silently into a single skill (not a new idea I know) that works passively. Here’s the skinny:

The thief gets a stealth score that is equal to their level/3, round up (max 3). In other words, it’s 1 from levels one to three, 2 from levels four to six, and 3 from levels 7+.

Instead of rolling skill-style checks, a thief adds their stealth score to any rolls made by creatures during surprise checks, For most creatures, a first level thief will surprise them on a roll of 1-3 rather than a roll of 1-2.

They also add or subtract their stealth score to the encounter distance: it goes from 2d6 x 10 feet, to (2d6 +/- Stealth) x 10 feet.

Finally, the thief also always get a surprise check separate from the rest of the party, representing their ability to hide in a crowd or duck behind a convenient shrubbery.