How to scale my hal ratiometric sensor output?
I know I can use an MCU to read this voltage and scale the output. But
is it possible to do so with no MCU?

Probably the simplest is this op-amp circuit: -

You need to create a 2.5 volt reference voltage and that could be from a potential divider from a stable supply voltage or, better still by using a voltage reference chip (if the supply voltages can vary a bit).
When Vin is 2.5 volts, Vout will also be 2.5 volts. If Vin rises (say) 100 mV, then the op-amp output lowers by 100 mV * R2 / R1. Thus you have gain (the ratio of R2 to R1). The output is inverting but that shouldn't be a problem.
So if R2/R1 = 10 when the input voltage is 2.6 volts absolute, the output will be 1.5 volts. If the input voltage is 2.4 volts, the output will be 3.5 volts.
You can also use an op-amp to create a non-inverting version: -

The gain of this circuit is 1 + R2/R1 so, if R2/R1 = 10, the gain is 11. So with 2.6 volts at the input, the output will be 2.6 volts. With 2.4 volts at the input, the output will 1.4 volts.