Should I start an Open-Source on my profile or my organization profile?

It... depends? I see the organization is your own and you are the only member. Are you planning to expand it? Is the open source project you mentioned relevant to what this org is about? If not, probably better to keep it under your personal account.

Something to consider is the nature of the copyright laws - i.e. which national jurisdiction - will apply. By my understanding that will be a matter of where you are rather than of the hosting platform. (Insert the usual disclaimer: I am not a lawyer - I'm just suggesting things for you to consider.)

Some countries have "work for hire" rules in their copyright laws. This is where things you do in the course of your employment are assigned ownership to the employer. While copyright is generally the same around the world, details like this do vary.

The same might go for arrangements other than employment, but I won't even speculate about that - let alone for other jurisdictions.

Certainly this can be a good reason to create software outside the organisation - and by using a suitable Open Source license there can be a clear grant so that the organisation is given appropriate freedom to use it as they need.

• As it happens, where I live, the laws are not entirely clear on that point, but my employer does state an explicit view that anything done on their equipment belongs to them.

Probably the personal profile first and you can make an organizaiton profile if it gets really popular

I would use the personal profile.

Your personal profile.