Shared folder data on another computer doesn't update when I modify it in my computer

File Sharing ≠ File Synchronization. Standard macOS File Sharing operates by letting a remote computer read or copy files over a network (via SMB), rather than keeping a live, two-way synchronized database or background file watcher. When you set a folder to Read Only, changes made on Computer 1 (M4 iMac) do not automatically stream or overwrite open files on Computer 2 (M1 MacBook Pro) in real time.

Why It Fails

• Static File Transfer vs. Live Sync: macOS File Sharing is designed for access/retrieval, not cloud-style synchronization. If Computer 2 opens a Pages or Numbers file, it reads a static snapshot of that file.
• Read Only Restriction: Because the share is marked "Read Only," Computer 2 cannot write back updates, and Computer 1 has no mechanism to push live document state changes into active open documents on Computer 2.
• Format Complexity: Pages and Numbers files are actually bundled package directories. Modifying them live across a basic network share frequently leads to caching issues or permission/lock conflicts.

There are a few ways to accomplish your intent, here are two (easiest first).

Use Apple’s Built-in Collaboration (Recommended for Pages & Numbers)

Instead of a network shared folder, use real-time collaboration:

• Open the Pages or Numbers document on Computer 1 (M4 iMac).
• Click the Collaborate button in the toolbar (or choose File > Share > Collaborate with Others).
• Set the permission to Anyone with the link can edit or invite Joan's Apple Account directly with Can make changes permissions.
• Both computers will now sync edits in real time through iCloud Drive. 

More info: Collaborate on documents in Keynote, Pages, and Numbers - Apple Support

Mount the Folder Live via Network (SMB)

Instead of copying the folder to Computer 2's hard drive, leave the master folder on Computer 1 (M4 iMac) and access it directly over your network from Computer 2 (M1 MacBook Pro).

On Computer 1 (M4 iMac - Host):

1. Go to Apple menu > System Settings > General > Sharing.
2. Click the Info (i) button next to File Sharing.
3. Turn on File Sharing, then click Options and make sure "Share files and folders using SMB" is enabled.
4. Under the Shared Folders list, click the + button, select your "Info for Joan" folder, and set the access permission to Read Only for Joan's user account.
5. Note the network address of Computer 1 (displayed in the sharing menu or under System Settings > Network). 

On Computer 2 (M1 MacBook Pro - Client):

1. Delete the old static copy of the "Info for Joan" folder from Computer 2's local drive so there is no confusion.
2. Open Finder and press Command + K (or go to the top menu bar and select Go > Connect to Server).
3. Type smb:// followed by Computer 1's IP address or local hostname (for example, smb://192.168.1.50) and click Connect.
4. Log in using Computer 1's username and password, then select the shared "Info for Joan" folder.

How it works now: Whenever you edit or save changes to the Pages or Numbers files on Computer 1, Computer 2 opens the live file directly across the network and displays the updated data immediately.

More info: Set up SMB file sharing on Mac - Apple Support

Thanks for taking the time to provide me with a terrific reply. I am going to attempt the SMB method since Computer 2 isn't connected to iCloud. We will see how it goes for me when I can get to it tomorrow, while following your excellent instructions.