I dosed H2O2 many times in my pico ~2g. All for hair algae control with my Carib Sea life rock.
I have dipped all my corals in it. As well as bathed the fish according to humble.fish guidelines. I've never seen ick, bubble algae, or aiptasia. For quarantine treatments it's been effective for many other reefers.
Target brand seems safe.
As for algae already in the tank, I have had overall positive results. But not always permanent removal for some types of algae.
At <1mL per day / 2gal, and xenia and GSP close up for a day. Doesn't seem to do anything for algae in the short term. This stopped the spread of new algae.
On several occasions, I've used 5mL / 2gal followed by a bubble bath then rapid 90% water change. This removed all algae for a time. The GSP / xenia retracted for almost a week. It did not irritate acans or montes. Inverts lived. No fish were in that tank.
Several weeks later, what I now believe to be bryopsis, returned to two spots low on the rock near the sand. The rest of the rock has been mostly free of algae since the first big dose. I have heard Carib Sea life rock is known for its persistent algae patches. They grow long and ugly. I've since tried direct application of peroxide, scrubs, supergluing over the algae, the glue peels off and the algae is still there!, urchin, mollies. Nothing ate it. Almost 3 years of this and I decided to use fluconazole. It's now been completely gone for two weeks. No negatives yet..
I still add a few drops of H2O2 when I remember or when I stir up the water/sand or scrub the rocks. I don't see the early stage hair algae or diatoms at all. I have yet to see hair algae in my 1 year old main display. Only my Carib sea life rocks were affected by the persistent algae.
I do add a heafty amount of peroxide, a good squeeze of the bottle when filling my ATO chamber on the larger tanks. This keeps the lines clear of bio film and it seems to provide some benefit with algae prevention, without shocking the corals. I have yet to see hair algae in my main display of 1 year (knock on wood).
I don't think I've harmed the beneficial bacteria as I believe enough lives below the immediate surface of the sand and rock that it would take significant amounts of peroxide to destroy. Though the irritation to fish and inverts is more my worry. Peroxide in your eye.. not a pleasant thought. This is why I followed the big dose with water changes.
Hope this helps.. If I ever see the bryopsis again, I won't be doing any mega dose of peroxide. Rather I plan to micro dose fluconazole, which Jason Fox said he does in an old interview.