sensor – I want to photograph in low light settings and make 11×15 enlargements, current smartphone not adequate

I have $350 US dollars to spend and was looking at new smartphones with top criteria being picture quality (have newborn, need pics).

However, I read even sub $200 cameras have better performance than phones costing $600. Plus, as a dedicated appliance, longevity seems better as well.

Are there small form factor(but good sensor size) cameras under $350 that can best say iPhone SE or Google Pixal 4a?
Criteria:

  1. Low light performance
  2. “Speed performance”/anti-blur
  3. 11×15 enlargements
  4. Optical zoom

In optimal light conditions, and optimal settings (little one standing still), current smartphone adequate.

If so, I will likely purchase cheap smartphone ($99) and upto $350 camera instead.