That floor part forms a wall of the box section and does provide strength to the side panels, it's one side of a triangle basically but it isn't a massive structural memember but that side panel would flex a lot more!
You could weld a new floor acroos to the side sill existing there but it may keep bursting through as its the seam between the 2 pieces and is usually filled with rust.
Personally I'd weld a new first ridge height side panel (the one with the fake seam in it) and weld the new inner flooring piece to that and patch the pillars. Seam seal it up and make it solid for years and years. Getting painted shouldn't be too expensive and then jobs done proper...!
