Pulling different voltages directly from AA alkaline cells wired in series
Can you do this? Yes.
Is it done often? Yes.
Should you? Probably not unless you understand how it behaves.
As the power draw drains the lower half of the battery pack, there will be voltage issues for the microcontroller, possibly reverse voltage into the drained batteries, and battery acid leaking. Not horrible failure with AA batteries but messy and annoying.
Depending on the current required, you could use the Arduino nano every's regulator. It has a compact single ic switching regulator MPM3610 with a max output of 1.2A at 90% efficiency. Not saying that you can or should pull 1.2A, but you said a few hundred mA. Especially with a low input voltage. The efficiency penalty is very low. Arduino says 7V minimum but its probably down to 6V minimum for proper 5V regulation so a 5x AA would power it just fine.
For longer run time just throw 6x AA at the arduino and power the leds from the regulator. The power cost vs runtime for the higher voltage is in your benefit.
Alternatively you can run the arduino at lower voltages. At 4.5V you skip the regulator and power directly. As voltage drops the max internal crystal and cpu speed are affected but you can switch it to 8 mhz via a setting in the arduino software, problem solved.
Or you can just throw an extra 1 or 2 batteries at it. 5x AA for the microcontroller and 3x for the LEDs.