Hah, that's interesting! Honestly square colliders might still be better depending on what other features/interactions you have planned (block pushing, maybe?), I just can't think of a lower-dev-cost solution to this edge thing than giving the character a circle-collider. I feel like retro games probably did rect-versus-tilemap collision math instead of using a physics system like Unity's, if you want to explore that route.  (It seem like Unity is giving every tile a square collider, then doing square-collider-versus-square-collider physics behavior here.)

If it helps, the easiest way I found to reproduce the edge-collision issues is to walk into diagonally into the top/bottom of a line of wall tiles. Keep holding the keys down to "rub" the character along the edge of the wall until you get stopped at the seam between two tiles. At this point, you can let go of the keys, then resume trying to walk horizontally in the same direction, but you'll still be blocked by the edge until you walk away from the wall.