The log-rank test is valid whatever the true situation with the hazards is. You are correct that only its power is affected. So if it rejects, then the hazards are not equal. If it does not reject, then you have to worry about the proportionality of hazards and power.

The principled approach would be trying to estimate the difference/ratio of the two hazards in a time-dependent matter. This is not simple, but doable. I would recommend the book by Martinussen and Schalke: Dynamic Regression Models for Survival Data, and the corresponding R package timereg. The support of a knowledgeable statistician would probably also be needed. Note that this is beyond standard survival analysis fare, so not everybody would know these techniques.

A last note: if the hazards are not proportional, then you just cannot have one value for the hazard ratio.

The log-rank test is valid whatever the true situation with the hazards is. You are correct that only its power is affected. So if it rejects, then the hazards are not equal. If it does not reject, then you have to worry about the proportionality of hazards and power.

The principled approach would be trying to estimate the difference/ratio of the two hazards in a time-dependent matter. This is not simple, but doable. I would recommend the book by Martinussen and Schalke: Dynamic Regression Models for Survival Data, and the corresponding R package timereg. The support of a knowledgeable statistician would probably also be needed. Note that this is beyond standard survival analysis fare, so not everybody would know these techniques.

A last note: if the hazards are not proportional, then you just cannot have one value for the hazard ratio.