You’re definitely not too old. I’d worry more about the gap and that your youngest may feel lonely. There are 16 years between my brother and I and although we love each other, it wasn’t until I was an adult that we had a close relationship, and it’s not particularly sibling like because we didn’t grow up together. Trying to find activities that are acceptable to an 11yo and a 3yo might be hard work too.
My parents were 39 & 40 when they had me, my brother became a first time parent at 47, and I was 40 when I had my one and only, so you are a positive spring chicken in comparison.
The grandparents aspect that a pp mentions is worth considering. Not so much not knowing them (I only knew one of mine, but didn’t feel the loss particularly), but about possibly balancing the needs of aging parents with the needs of a young child. My parents are now in their eighties (and still going fairly strong) and I have a 3yo so I think the next five years or so are going to be quite demanding for me personally. Hopefully my dd might break the cycle and pop out some kids in her twenties!
I think yearning for another baby in your late thirties is fairly common, probably hormonally driven. But really, when all your kids are getting independent and you’re a world away from nappies, sleepless nights, soft play etc etc, do you honestly want to reset the clock again?