The waste from a walk-in low threshold shower tray will be fitted under the floor [below the bath outlet connection to the soil stack] unless you go for a raised shower tray to use the existing bath connection, stepping up onto the shower tray by 100mm or so? The setting out of the tiling round the bath looks like the bath is a standard 1700x700 bath- you can get a shower tray that size.
You can also get shower trays with a curved front edge on the shower head end which will give you a bit more space - the door doesn't need to open fully but that won't matter too much as few people open the door into a room out to 90 degrees anyway [you'd need a door stop on the floor to stop the door's handle smashing the glass. [Mira one 1700x710 - link attached:
https://www.victorianplumbing.co.uk/mira-flight-right-hand-walk-in-shower-tray] Click on the product dimensions to see the 1700x710 purchase code- this one's from Victoria Plumb but you can shop around for the cheapest supplier. They'll do a matching shower screen- you won't need a door in or out as the screen will enclose it well enough so splashes won't clear the walk-in part. You can fix a seat to the back wall providing you insert a bracing ply panel behind the plasterboard if it's timber stayed partition before you put the tiles on below the bath edge. If it's a solid wall even better!
Probably worth checking that you can still get the same tiles!
Good luck!