Do you also drink your pond water, or is it just for baths/showers and washing dishes?
One of your easiest solutions would be to use a pond dye. Here is a link to one of the popular products.
Aquashade Info SheetThis product is safe for swimming, irrigation, and animal consumption (which usually means watering livestock).
It is perhaps safe for human consumption, but who knows how expensive that testing would be for the manufacturer plus their potential legal liability for a human death, so it is wiser for the product label to just say "No." (However, I wouldn't drink it, since that is what the label says.)
There are several people on Pond Boss that dye their ponds and use them for family recreation. I would assume swimming is more exposure than a bath (since you frequently dunk your head), but people typically don't swim every day.
Likewise, there are some algaecides and herbicides to use in ponds that have similar label restrictions.
I think using the dye and then some rare, targeted herbicide treatments would probably give you some worthwhile improvements. Maybe do the harshest treatment when everyone is leaving the house for a few days?
Perhaps use the search function to read some of the pond dye threads.
Hopefully, some of our actual experts will drop into your thread.
Good luck on your pond improvements!