You will need to cut away the tape back to a firm edge with a sharp knife and remove it - it's probably paper corner tape which runs 90° around the corner and onto the wall, so you wont be able to replace it. Once removed, sand the edges of the paint flat, fill with a good quality fine surface filler if necessary and repaint. Apply a bead of caulk along the ceiling/tile joint and then paint - mist coat the filler first and then use a neat coat or two to get an even finish. You could use a bead of silicone rather than the caulk, if you prefer, but do this after painting.
Moisture penetrating the paint is a likely cause for loosening it so it would be wise to use an acrylic eggshell/bathroom paint to prevent any further problems.
Standard Toupret ready mixed filler (which is good as a fine surface filler) would work fine for that job but any quality branded fine surface filler would be fine - just avoid the cheap brands.
Yes, the caulk/silicone will help prevent cracking but you won't need both - it's either/or in this instance.
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