Is it possible to vent a tank water heater horizontally through a wall and terminate just outside that vertical wall? I realize there are other restrictions as far as overhangs and openable windows, but can the vent pipe run horizontally ( about 7' ) at the 1/4" per lf of rise, or does the code require a power vent? Can you even put a power vent on a tank water heater?

You seem to be asking about an atmospheric vented water heater. Yes, it can be vented horizontally out a side wall but there are strict venting requirements in doing so.

A water heater vented by means of a powered vent is called just that: power vented water heater. It is more ideally suited for horizontal venting out a side wall.

I'm going to say, for the most part, no you can't terminate the vent right where it exits the wall. If the water heater manufacturer states you can, in the installation instructions, then you can, but I don't recall any saying that's possible(unless it's a direct vent model).

California Plumbing Code states -

510.5.2.1 A chimney for a residential-type or low-heat gas utilization appliance shall extend at least three (3) feet (0.9 m) above the highest point where it passes through the roof of a building and at least two (2) feet (0.6 m) exceeding any portion of a
building within a horizontal distance of ten (10) feet (3.0 m) (See Figure 5-1). [NFPA 54: 12.6.2.1]

510.5.2.3 A chimney shall extend at least five (5) feet (1.5 m) above the highest connected appliance draft hood outlet or flue collar. [NFPA 54: 12.6.2.3]

Your codes might state otherwise...

if it was legal why would they have a powervent then?

I don't know the details of the answer, but I know it must not work because there's powervent water heaters to do what you want

You do not "put" a power vent on a water heater, you buy a water heater with a power vent installed on it. If you were to vent through a side wall, you would create many problems with the combustion, depending on which way the wind was blowing.

Those requirements are part of the regulating body and are UNIVERSAL to every area.

10-15 years ago i installed a power vent onto a conventional gas water heater.
i was a tjernlund made specifically for that purpose.
i had to remove a plug on the gas valve port labeled 'pressure' and connect a piece of tubing from that port to a pressure sensor port on the blower control. when the thermostat called for heat, the gas valve opened and sent pressure thru the little tube signaling the fan to turn on.
i looked on the tjernlund site but did not see this power vent listed.
P/S, i don't remember much about how else it functioned.

The modern ones use an electric ignition instead of a pilot light so the burner does not come on until the damper is open.