Water-bird that can take off vertically from the water?
Yes. A duck can be observed taking off near-vertically from the water's surface in this video. Watch the first duck to take off (from about 0:08). Immediately after take-off, the duck has a very low horizontal speed, and works to gain speed by a combination of flapping and vertically beating its tail. The full process is as follows:

Beat 1: The duck gives a sudden start. Both wings are beaten once on the water's surface to take advantage of the extra resistance the water provides, compared to air. The duck presumably also pushes down on the water with its feet below the surface in order to gain extra lift, but this is not visible.

Beat 2: By the start of the second downbeat, the duck's body is clear of the water, but the feet are obscured by spray.

Beat 3: The whole duck is clear of the water, and is gaining some horizontal speed. This wingbeat is accompanied by a clear vertical flap of the tail.

Beats 4 onwards: The duck continues to accelerate horizontally, remaining clear of the water.

Because the duck comes near-vertically off the water's surface, and remains airborne thereafter, I'd define the take-off as vertical, and the subsequent flight as transitioning into a duck's normal near-horizontal flight. Similar take-offs by terns can be seen in this video (but starting from a dive under the water's surface, see from about 1:02).

More generally, many waterbirds can take-off vertically from the water's surface, without requiring a run-up. All that is generally necessary is to face into the wind, and spread their wings. If the sea-surface is basically stationary, but there is wind, then any difference in speed between the air and the water can be exploited to generate lift.

If there is no effective wind (i.e., the water and the air are moving at the same speed), then the birds have to generate the lift for take-off by expending energy. Some species can do this, but it gets harder with increasing body-mass and wing-loading. I have personally observed a juvenile frigatebird (a species that generally weighs around 1 kg, but with very low wing-loading) lifting off vertically from the water's surface on a windless day. Note that frigatebirds would not normally land on the water (their feathers are not waterproof), and trying out a water landing seems to have been a play behaviour on the part of the juvenile.