I think I got all the positive-yard self-passes, but there are some that may have occurred way in the past that I missed. Football-Reference stops keeping detailed play-by-plays around 1994, so from Harbaugh down, I only counted the ones that I could confirm happened via the box score, but there are some that may have occurred but were unverifiable.
Only two have been caught for touchdowns, three were in the playoffs, but only one in the playoffs AND for a touchdown (the Mariota one that sparked the question). Most were for single-digit yards, but the longest was for 20 in 1959 from Milt Plum. Drew Brees has the most positive-yard self-passes in his career with 4.
Here is an image:

Since there is no table markdown in Stack Exchange, here is the lists specified to OP's request. Since the image has more detail, I am leaving it up.
QBs which have passed to themselves for positive yardage:
- Johnny Unitas
- Lamar McHan
- Y.A. Tittle
- Milt Plum
- John Hadl
- Sam Wyche
- Tommy Kramer
- Richard Todd
- Dave Krieg (2)
- Bernie Kosar (2)
- Bobby Hebert (2)
- Vinny Testaverde (2)
- Steve Young
- Jim Harbaugh
- Bubby Brister
- Brad Johnson (TD)
- Jake Plummer (2)
- Kent Graham
- Steve Strenstrom
- Donovan McNabb (3)
- Trent Green
- Marc Bulger (2)
- Joey Harrington (2)
- Steve McNair
- Aaron Brooks
- Michael Vick
- Drew Brees (4)
- Kurt Warner
- Matthew Stafford
- Jimmy Garoppolo
- Sam Bradford
- Carson Wentz
- Alex Smith
- Marcus Mariota (TD)