dnd 5e – How do I rebuild a damaged Eberron construction?

There is no RAW for what I could find, so everything that is listed below depends on your DM, but here is my interpretation based on the Eberron configuration and the material currently published for Eberron.

In Eberron, almost all the constructions and others are made by the Cannith house or one of its authorized workshops. So, if you have a broken automaton, it would be logical to go to the workshop / enclave of the nearest house and ask about repair services.

The fact that you also need to reset your programming only enforces this need to find an expert, since simply fixing all the broken parts would mean that you would get the same entrenched enemy that you have already defeated.

Determining the cost is difficult, and may be up to the DM, but I would suggest that the House of Representatives request a service instead of gold. This could be anything from looking for rare materials needed for repairs to a job that Cannith should do and consider to have an equivalent value.

If you want to do it yourself, or avoid House Cannith, you can try some repair tool controls to fix it and at least a very difficult control to correct your programming. Instead, you might find an independent Architect and expect him / her to have the skills for the job.