Where to look for data that is stored somewhere in the browser? And how to look for them?

Question

JavaScript

I noticed on one site that if you use its functionality from one browser, after using it you get a ban for 2 minutes (it seems to be done so that the server does not load), but if after that you repeat the procedure from another browser, you will be able to bypass this ban and use the functionality again . But the ban is still issued after each use of the site's functionality, but each browser has its own time (countdown).
I would like to know how to conduct research in this area in search of either cookies in which it can be stored and in what form for substitution, or in localStorage, which I generally only found out about today, or somewhere else. In general, my goal is to remove this race restriction, it is still stored on the client.
PS After restarting the browser, the countdown still continues.

Answer 1

Most likely, your case is simple, as Aleksey has already described.
Your browser in each request passes the User-agent field - a string describing the browser, usually unique for each browser, and, of course, your IP. The server remembers you in the session conditionally as

"1.1.1.1:Mozilla/5.0 (iPhone; CPU iPhone OS 5_1 like Mac OS X) AppleWebKit/534.46 (KHTML, like Gecko) Version/5.1 Mobile/9B179 Safari/7534.48.3"

Change the browser OR IP - and you will no longer be recognized (if this is your case).
Of the other methods, there are:
cookies, localstorage - you are already aware of them.
Of the more cunning - javascript can use cache, browser features, installed add-ons, etc. - there are many options here.
There are also flash cookies, and the rarest, probably java.
Read about evercookie
To visually delve into the request-response, use Firebug.

Answer 2

To search, it is first desirable to know what to search, that is, what kind of data stored in the browser is sent to the server, for this use Fiddler, Wireshark, etc. sniffers.

Answer 3

Ban is issued either by cookies or by IP + USER_AGENT.
I am leaning towards the second option.
It is easy to check - you got a ban, cleared the cookies in the browser, if the ban has disappeared - it is based on cookies.
If not disappeared - to IP + USER_AGENT.