What is the SEO impact of the multiple redirects that return to the current page after setting up a cookie?

If you can figure out how to do this configuration without the redirects, it would definitely be better.

Note that you probably also have a redirect from http to https, so it's a total of up to 4 redirects to get the user where they want to go. If the user has a high latency, this could be as long as several seconds before his page, even begins load.

As for SEO, as long as your redirects continue to work without cookies, googlebot will follow them as a web browser. However, Google takes into account the performance of the page in its classifications, so it is logical to think that a redirect configuration that reduces performance could also affect the ranking of a page.

Is there any practice / practical experience that people have with this type of chain redirect?

It is possible (in fact, very likely) that this chain redirection configuration is a design standard with which I have not worked or listened. However, I personally would tend to strive for zero redirects on my pages as long as the URL of the request is correct.