Our shower has no screeded base, just tiles glued to floor, therefore no slope to drain. Screen sits on top of floor however where the door opens, significant water pours out, creating a huge puddle under the vanity (no drainage in bathroom ugh), obviously the lowest point. Previous owner (& dodgy renovator) siliconed small tiles at an angle to try and hold water in however it's completely ineffective. I was considering whether we remove screen, cement or glue some kind of brick or paver surround, tile over, then reinstall the screen to prevent this? But am open to ideas!
Saw previous posts regarding placing a lip in front of shower, but they used a curtain and it would block our door.
Welcome to the Bunnings Workshop community. It's great to have you join us and thank you for sharing your question about your shower.
Your proposal of removing the shower glass doors and building a tiled surround is actually a sound idea. But it does not fix the fall inside your shower. In order to properly fix it, the tiles must be removed and a proper screeded angle must be made and then tiled over. This will give you the proper fall to drain the water from your shower.
If you proceed with the surround and do not fix the fall, just be aware that water will puddle inside the shower area. Please remember to make sure that the surround is strong enough to hold the weight of the glass panel when it is re-installed.