I'd reframe what your task is. Your task is not explaining what should (not) be done, but helping both of you get a clear picture of what the situation (goal, challenge, problems, risk, etc) is.
If you made things clearer for both of you, you can feel good about what you did. You helped the other person make better choices. Now this still can be something different than your choice. But if it's their responsibility, then that's fine.
In situations where I don't agree with my boss or colleague I focus on two parts:
First; do we fully understand each other? Are we aiming for the same thing, and do we agree that X, Y, Z are risks? Are there other aspects you perhaps didn't know that are important for the other to weigh, etc.
Second; what is the earliest we can test who's right on the important part where we differ. You can suggest a short brainstorm for a proof of concept, etc.
I think all of it just doesn't fit very neatly to this type of framework. It's a combination of very many things, different teams, systems, legacy systems, lack of data, bureaucracy, politics, so it is overall just very messy. In many cases it feels impossible to make others understand what the true risks are if they are not intimately familiar with everything that's going on. It's the kind of thing like, not sure, if you've seen Krazam videos, but the one with Galactus (microservices). You kind of have to explain why some simple thing can't be done or some seemingly simple thing is just way too risky or time consuming.
I would actually rather not work on something like this, but it pays more than anything else I could currently get.
If you made things clearer for both of you, you can feel good about what you did. You helped the other person make better choices. Now this still can be something different than your choice. But if it's their responsibility, then that's fine.
In situations where I don't agree with my boss or colleague I focus on two parts:
First; do we fully understand each other? Are we aiming for the same thing, and do we agree that X, Y, Z are risks? Are there other aspects you perhaps didn't know that are important for the other to weigh, etc.
Second; what is the earliest we can test who's right on the important part where we differ. You can suggest a short brainstorm for a proof of concept, etc.