Depends on the concentration of the HP you have as it can come in a few forms. The strength is key. The typical store bought bottle at a CVS type store is 3% and you can use that strait (recommended) in a dip for 2 min. 6%, cut it 50/50 with RO water, etc. Confirm your bottles concentration! Can assure you people have just followed directions online without noting this detail and ended up doing more harm than good. You can get HP in 33%, 40%, 50% quite commonly which could end up 10x + the dosage.
Look up what people have used in on successfully and what dosage as that likely keeps changing as people experiment. I have has success with Zoas and Acans (3% up to 2 min) and have dipped every one I have added to tanks as a preventative. It takes the place of a FW dip for me. I have lost some corals doing this but also lost some not doing this as well so I can't blame the HP directly as any new frag can melt on you. Be careful of anecdotal evidence by others that may have made the mistake above and not admitted it. Zoas/acans should look recovered the next day or so. Not done a branching LPS like in the OP photos so no experience there. I would cut that base off, scrape it and paint/dip the skeleton only to be on the safe side unless you can find success by others online.
HP is really useful for the tank. You can paint it on target areas, sterilize frag plugs and also drain your tanks to spray/paint in on nasty algae areas like "confined" areas of Bryopsis, then just refill the tank assuming you don't spay a ton and its not a tiny tank like a nano. (kills the algae vs distributes the algae) The HP will dilute enough to be safe and quickly reacts with your tanks water when you fill it back up assuming you Don't over do it. It is H2O2, so the tank water will strip that O molecule off. It's not like a poison, it just oxidizes (which is why it is
terrible for wound treatment despite what grandma says). I have used it directly in FW shrimp tanks to knock out the pest algae and keep the desired tank plants/shrimp alive but have since forgotten the dosage strength and would need to look that up.
DO NOT use it on SPS or anything else you would not use a FW dip. Your plug will also be bleach white after like cleaned bed sheets, so know that as well as it is basically "OxyClean" without the washing sodas.