SharePoint says I don't have access when I log in from home

Yep, that's almost always the personal account winning. Quickest test: open a private/InPrivate window, go to SharePoint and sign in with the work address. If the sites open there, the permissions are fine and it's just the browser. To fix it properly, either sign out of the personal Microsoft account everywhere in that browser, or make a separate browser profile just for work and only ever sign in to the work account in it. Edge is good at this, it lets you tie a profile to the work account so it stops guessing. Also check Settings > Accounts > Access work or school in Windows, adding the work account there helps the Office apps pick the right one too.