How can I make sure my Mac has access to files on its own SMB server?
This is the reason why companies set up shared directories - to allow or deny group read / write permissions to files.

You will want to think about how you wish to have people authenticate and whether all shares can default to everyone can write.

On the Mac - files like this typically are homed in /Users/Shared so you could move those files to a place that’s naturally open to all accounts or change the permissions on the files you chose to share from the sharing panes.

Another last bit of advice, spend a little time thinking if you can use POSIX group / ID based permissions or want to layer on Access Control Lists (abbreviated ACL) that are more granular and can do things like add a group and then deny one member of that group from files and folders.