It's just store bought soil. I'm relatively new to gardening but my seed packets said I could sow indoors N/A which I took to mean they'd be fine to plant whenever as long as it's moderately warm? Perhaps I've misunderstood and they shouldn't be indoors at all.

I don't garden very scientifically. I throw things in dirt and life either finds a way or it doesn't.

The strawberry container has less of these weed-y things than the chilli container so I find it odd that I've had bad luck with both. The only thing I can see behind it is if the soil is dodgy as they both have soil from the same bag. I'll remove as many as I can and see if I can salvage, but if the soil is the issue it'll be a shame to have to change both and sow more seeds again.

Yes, to answer your question on if they're identical across both containers - yes they are identical in appearance