Does the peer review reciprocity principle apply globally or per venue?

First, I'd say that your obligation* of peer review is to help your community of peers, not specific venues or publishers. It's the peers that do the reviewing mostly for free, and their work you're supposed to reciprocate. Hence the principle should apply globally.

However, spreading your efforts out a bit can be beneficial, leading to more diverse reviewer pools for a given journal. (And hence a higher chance they can find the ideal person to ask.) And of course, you're free to focus your efforts on reviewing for journals you particularly like, whether for their quality, (possibly also unpaid) editors you have a good relationship with, or other reasons.

Second, aiming for a close balance in reviewing efforts given and received seems misguided. Focus on writing useful reports, not on the amount of work (that of others is hard to estimate anyhow). You can't really review more than you're invited to review, and even then it's certainly better to decline if you can't produce a quality review in the expected standard time frame than accepting each invitation in a vain attempt to cancel out review work you've received already.

*If obligation is the right word. I tend to think of 'obligation' as a requirement, whereas this reciprocity is more of an 'ought' in my opinion. But hey, different definitions exist.

I think you are defining "reciprocity" too narrowly. And a definite answer to your direct question would be misleading.

In general, the people participating in an academic field form a community and as a community they contribute to it. But people contribute in different ways and in different ways at different times depending on their skills and circumstances. Note my underlying assumption that you don't work in a field solely to advance your own career, but to advance the state of knowledge for everyone.

Some people are, for example, good researchers, but poor reviewers. Perhaps they don't have the time or the temperament to be helpful. They best contribute to the community via their research. Other people are the opposite. I was once in a situation in which it was impossible to do much research but I still understood what was important and could still review. Yet other people have a more balanced approach.

One other issue is time. At different points in a career, people can contribute in different ways. A young researcher probably needs to focus more on production than on helping others, just to increase the chances of advancement. At other times, perhaps later in the career, a person has lower output, but still needs to keep abreast of what is happening in the field, and so reviews current work.

But there are other ways to contribute other than reviewing. Conference committee work, for example. Advising younger researchers (students) is an obvious contribution.

To come to a more definitive answer to your question, though, if you publish a lot of papers at a conference, you become more closely aligned with that community, so you are more likely to be asked to review there. Probably you will want to accept. I don't think you owe any allegiance to a commercial publisher, however, even if you publish with them frequently. But you might want to "help out" some particular editor who has been helpful to you in the past. But note that my examples here are more in the realm of personal, rather than professional, obligations. But I don't think that in most cases, other than the most extreme, that it is an ethical issue.