To start with “push button start with a toggle switch” can’t be done, they are different switches.
So to give you a push button function to start the engine instead of moving the ignition key to position three you will need a non-latching push switch and wired in parallel from the brown wire at the existing ignition switch to the white/red wire feeding to the starter relay from fuse 17, so its just a wire overlay. Simples
The operation is with key in the ignition switch at position two, the button is pressed the relay operates and engine will crank and start, allow button to release.
You will still need to remobilise the engine with the fob.
You may also feel that it would be nice to have an illuminated button, some illuminate on press other illuminate to aid location of the button, of course both modes will require an additional power supply.