Shower Floor Tile – Please Help!

If the liner is good you don't need to go down more, though if you replace with the same size tile it may crack in the same place if there's a (evidently) structural issue there.

I'd be inclined to fill the hole with an "accent stripe" of 1" tile so the crack (when it re-cracks, as seems likely) can follow a grout line rather than crack the face of a tile.

Vacuum it out, preferably with a Wet-Dry or Shop Vacuum that has a thin nozzle attachment applied parallel with the seam or a floor sealing Water Pickup attachment applied perpendicular to the seam. To assist this operation you can tape the seam so the vacuum's seal is concentrated. A bag-less vacuum can work just as well, but be careful not to fill it more than 1/3rd & damage the vacuum or electrocute yourself.

If those don't get most of it or neither are available to you then a thin towel or cloth, like bed sheets or clothing can be stuffed into the seam with a putty or butter knife to soak up & wring out until dry or mostly dry. Avoid paper towels as they can easily rip & are a pain to straighten back out repeatedly.

Then, let it air dry. If you need to use the shower then just duct tape the seam to keep water out for one. But for another, to see if the water is coming from somewhere else & the seam is filling up again. If it's unchanged then keep taping & un-taping until it's bone dry.

Finally, actually fill-fill the seam with caulk & force the caulk in with your finger. Don't bother trying to get it perfect the first time, instead come back in a couple of hours & do a second application of caulk to get the caulk flush to both the floor & wall. Then, don't use the shower for at least 6-hours. If you can't wait that long or longer then tape OVER, as in bridge, but don't tape ON the caulk.