The polymeric clarifier would have been caught in the filter and then removed by backwashing (since it sounds like you've got a sand filter). That would have also removed most negatively charged particulate matter including some algae. Chlorine would have fully oxidized ammonia, urea, and some other nitrogenous compounds into nitrogen gas and carbon dioxide that will have mostly outgassed. Some other organic compounds will get partially oxidized and remain dissolved in the water. Some others are volatile and would outgas. Many won't react with chlorine and will either remain dissolved (including salts) or will be insoluble so will either form scum at the surface or will have been handled by the clarifier.
The thing to remember is that though algae is unsightly, it is not itself a health hazard (unless there is so much that you can't see the deep end or that it is on surfaces and is slippery). The result of clearing the water doesn't result in toxic compounds remaining. The vast majority are innocuous and in small quantities. There are some disinfection by-products from chlorine oxidation, but the amounts are relatively small and in an outdoor residential pool exposed to UV from sunlight it tends to be minimal.
As for the Green to Clean and Yellow Out, these are sodium bromide products so have essentially turned your pool into a bromine pool. Over time, bromine will slowly outgas from the pool and some brominated organics may get caught in the filter and backwashed, but given how much you've added to the pool that could take quite some time (i.e. years). So when you add chlorine to the pool, it is getting used up converting bromide to bromine -- hence, you've really got a bromine pool right now. 14 pounds of sodium bromide (assuming these products are pure sodium bromide) in 26,000 gallons (40' x 16' x 5.5' average depth) is 64 ppm bromide so not a small amount. That's the worst part of the advice that you were given from the pool store. Now bromine is a sanitizer like chlorine, but it is not protected from breakdown in sunlight so you may find that your chlorine usage goes up on sunny days compared to before. Bromine also smells a bit different than chlorine (actually, I'm referring to bromamine smelling different than chloramines since that's what you smell when bromine or chlorine react with the ammonia from your sweat from your skin).
So your pool is safe, but is no longer a chlorine pool -- it's a bromine pool.

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