[trying out ChatGPT] ZyXel GS1005HP PoE Switch repair - scorching hot coil

[faekjarz]

Gidday, Daves! 
You're all Daves, as far as i'm concerned.  …lovely stuff 

I'm repairing a ZyXel [CyCell, CyberCell] Switch, a GS1005HP with PoE+ feature.

Symptoms:
scorching hot coil/inductor (part of the 57V PoE supply circuit), beyond 160°C, adjacent components heat-affected

For the fun of trying out shiny new tech, i've attempted to figure out the correct coil/inductor, using Microsoft Copilot (ChatGPT). The results are not exactly meaningful, for a novice like me. I've documented my rather turbulent ride on the Fediverse (aka Mastodon), see also the related thread https://layer8.space/@platymew/112043595783702798.

I do live in Germany, but i'm asking in general: which coil/inductor would qualify as a proper replacement part.

If i recall correctly, the guy in the (German, Austrian accent) Video used a 100µH inductor. Even the OEM/ODM left a comment in their Video, mentioning a known issue with certain batches. They didn't quite explain what the actual fault was, though.

I'm looking forward to your comments and thoughts.

(I intend to re-sell the fixed item on eBay, so my quality standards are quite high - it needs to be reliable - i intend to replace the heat-affected parts nearby as well.)

EDIT: the point is, that i really don't know enough about ferrite coils / inductors. The droids i'm looking for have 2 leads, 2 poles, ~13mm diameter, a width of ~6mm, and an estimated up to 1mm² conductor.