I don't think it's supposed to -- it's reserved by your browser. You can use shift+click, but generally speaking larger operations are just going to work better in the Desktop app
I can't use the desk top app because it's synced to one workplace account and there is no unsync option when I try to unlink that one. What I want is to have two separate accounts so that I can use one for one job, and a different one for another job, but it won't let me. I can now use a web version for one account, but can't sync it to my personal desktop account because it has synced to an organisational account and the rfe is no 'log out and log into a different account' option!
There is currently no option to select all items in the web library. We might consider adding something like this, most likely as a toolbar button. However, as mentioned above, working with a large number of items in the web library is very inefficient.
If you're okay with having a slightly more complex setup, you could try running multiple Zotero profiles.
Upgrade Storage
If you're okay with having a slightly more complex setup, you could try running multiple Zotero profiles.