I do not know the exact answer, but I'm pretty sure you won't have a problem going from one desktop to another. I do not believe the information is stored as a cookie - it would be a miniscule file, and I'm sure those notes are stored on the server.
Btw, I copy my analysis and paste it directly to Notes. I don't bother to space it out, since it isn't that hard to read anyway.
Apparently one answer is 'at least 45k'. I seem to have saved that much in the text for the notes for one game. I should probably erase it because there could be a limit on the total text for an account too.
Duh! Here is how I managed to confuse myself. I may be somewhat spacy, but this is pretty easy to have happen if you have a lot of windows open or leaving it and coming back later ...
Go to an online game. Look at the Notes there. Open an analysis board. Edit the notes there, and save them. Close the analysis board. Look at the notes on the main page for the game. Oh no, where did my notes go?????
You just have to reload the main page, and they will be there. It took me awhile to figure that out, too.
Another way to handle it is to just copy the moves from analysis, and then close the analysis window and paste them in the main notes. Not necessary, but it's nice to actually see the notes working!
Why don't you just write them down on paper brah that way your notes can't be hacked brah