Is it possible to have only my work-related bookmarks show up when I log in to my work Chrome account and only my personal bookmarks show up when I am logged in to my personal Chrome account? Now they all show up in both accounts.
Sure, just add new users to Chrome:
Do the above twice to create users named Home and Work, and associate them with the corresponding personal and work-related Google Accounts.
To switch users, just click the icon on the top corner of the Chrome window or press Ctrl+Shift+M to select the user. No icon will appear if you only have one user associated with the browser.
Note: If you do the above and still find each user displaying the bookmarks of the other, you may have synced back online from the PC a mixture of bookmarks from both accounts. In this case once you have two separate users set up in Chrome and associated with two separate Google Accounts, you should be able to switch to User 1 and delete User 2's bookmarks, then switch to User 2 and delete User 1's bookmarks. Henceforth the two accounts' bookmarks should stay separate due to the separation of users in the browser.