Load Bootstrap CDN only if not is loaded before from another project
One approach:
Attach the modal-page-bootstrap library as you are doing, and don't also load bootstrap.js in another way.
Don't worry about adding libraries multiple times to the same page. Drupal is smart enough to only load that library once, and at the right time and order.
The conflict will only arise if you are loading bootstrap.js some other way besides attaching a library. If this is the case, then as @leymannx says above you need to find where the extra bootstrap is coming from.
If the Bootstrap CDN is loaded by a script tag in a Twig template, just remove that script tag and only load the CDN via the library, allowing Drupal to keep track of it.
Another approach:
If another_project is a theme or contrib module, then it has probably already defined the Bootstrap CDN as a library. If this is the case, you could just attach that library wherever you need it to prevent conflicts. Take a look at the another_project.libraries.yml file to see the name of the library, and then load that library wherever you need it in your custom theme or module. Again, as above, this will allow Drupal to manage the library so that it will only be loaded once, and only where it is needed.
Note, however, that by doing so you will create a dependency on another_project. If you do this in a custom theme or module, then you should make that dependency explicit by declaring the dependency in your info.yml. Otherwise, if another_project is not present for any reason, you won't be able to load the library.