Whether they are 'established' or not isn't really a consideration because they are growing in a pot. This naturally restricts the ability of the roots to seek out water, as they would in open ground, so they will still need watering ongoing as necessary. Otherwise, two things that are likely causing issues:-
You say the pot is in 'full (but indirect) sun'. This is a contradiction in terms - full sun means direct sunlight, indirect sunlight means shade. These plants need a minimum of six hours direct sun a day.
You have the pot inside an outer container which presumably does not have drainage holes. Unless you remove the plastic pot when you water, it may be that water builds up inside the outer container and the bottom of the plastic pot is sitting in it, causing the soil to be too damp for too long, or conversely, any water sitting on the bottom of the outer pot may not be in contact with the plastic pot containing the roots (I can't see how deep the plastic pot is,but can see the outer pot is narrower at the base), and that water will turn 'sour' over time. If there is a gap at the bottom where water may sit, it would be better to use a wider outer pot to accommodate the inner pot properly.
It also looks as if there may be too many plants in the one pot, which might mean they don't have enough root room. They also do not like being disturbed or moved and may not respond well to being split up, though you could soak the pot and try to reduce the contents by pulling extra ones out and discarding them if there are too many. They do best in deeper containers because of their tap root - as already said, I cannot tell how deep the plastic pot is.
At this time of year, your days will just about be slightly shorter than night hours - as this process takes place and proceeds, these plants tend to stop growing and may die back or simply go dormant, so you may well not see flowers this year. Further information here https://www.gardeningchannel.com/how-to-grow-california-poppy/, with a section on how to grow in containers towards the end.