Errors are thrown when assigning Input Actions Asset that contains a custom InputProcessor or InputBindingComposite as Project-wide Input Actions

Reproduction steps:
1. Open the attached “BugReporting” project
2. Open the “Assets/Scenes/SampleScene.unity” Scene
3. Select the “Settings/Controls.inputactions” asset
4. In the Inspector Window, click the “Assign as the Project-wide Input Actions" button
5. Enter the Play Mode
6. Observe the Console Window

Expected result: No errors are thrown
Actual result: Multiple “No InputProcessor with name 'Rotate' (mentioned in 'Rotate') has been registered" errors are thrown

Reproducible with: 1.8.0, 1.8.1 (2022.3.24f1, 2023.2.18f1), 1.8.1 (6000.0.0b14)
Could not test with: 1.7.0 1.8.0-pre.2 (2022.3.24f1, 2023.2.18f1) (The “Assign as the Project-wide Input Actions" functionality is not present in this package version), 1.8.1 (2021.3.37f1 (The “Assign as the Project-wide Input Actions" button does not appear))

Reproducible on: MacOS Sonoma 14.4.1 (Intel), Windows 10 (user’s)
Not reproducible on: No other environment tested

Notes:

• The user reported that when the built Player is opened on an Android device, a crash occurs. This behavior was not reproduced locally by the CQA