I guess one problem may be that you selected features for an l4, as in the template. This is a Cortex-M4, and uses the target thumbv7em-none-eabihf. In your case, select the features related to the l5, which is a Cortex-M33 (target thumbv8m.main-none-eabi). So add the target: rustup target add thumbv8m.main-none-eabi
and use in the Cargo.toml features ["l552", "l5rt"].
Additionally, make sure you are using the correct GPIO connected to the LED in your board (which may be different to the one in the template).
I hope this helps.
Edit: I see that the STM32L552ZE does include a FPU, so the target you are using thumbv8m.main-none-eabihf should also work. Not required for this simple LED application, though.
Edit 2: see the features., available in the latest version 1.6.2 of stm32-hal.
I've changed the features and updated with l5 and also connected the LED pins correctly but still I've the same issue.
let gpiob = &peripherals.GPIOB;
gpiob.odr.modify(|_, w| w.odr7().set_bit());
Really dumb question: have you configure your GPIO B7 as an output? It would be helpful if you post the contents of your main.rs.
Alternatively, can you try flashing this example on your board and see if your LED blinks?
You need to use the GPIO connected to the LED in your board.
That is, in your main.rs, line 42, replace: let mut led = Pin::new(Port::C, 13, PinMode::Output);
with this let mut led = Pin::new(Port::B, 7, PinMode::Output);