Detailed repro steps:
1. Create a Unity Project e.g. with the 3D template
2. Connect it to Perforce in the usual way
3. Mark Assets/Scenes/SampleScene for add (context menu in Project tab, "Version Control" -> "Mark Add")
4. Submit the pending changes "Window" -> "Asset Management" -> "Version Control"; right click on the default changeset and "Submit..."
5. In P4V, locate your project in the Depot view, open the context menu and select "Branch Files..."
6. Choose an appropriate branch name "Choose target files/folders:" e.g. Source: "//depot/BranchTest" target: "//depot/BranchTest2"
7. Press the "Branch" button
8. Still in P4V, "Get Latest Revision" on the new branch in the Depot view
9. Open the new project in Unity (BranchTest2)
10. Set the Perforce settings again in Project Settings and connect
11. Duplicate Assets/Scenes/SampleScene, this should create a new scene marked for add automatically
12. Modify the original SampleScene (add a cube) and save it
13. Open the Version Control window again
14. Observe that "SampleScene" is open for edit
15. Observe that "SampleScene 1" is marked for add
16. Submit the default changeset with these in it
17. Close Unity. Switch back to P4V
18. Open "View" -> "History", find the changelist you just submitted in BranchTest2 (select that branch in the Depot view to filter, as path filtering is probably on)
19. Right-click on the changelist, select "Merge/Integrate Using ..."
20. Change "Choose target files/folders:" to your original branch e.g. "//depot/BranchTest/Assets/Scenes/..."
21. Hit "Merge"
22. Look in //depot/BranchTest/Assets/Scenes/ in the depot view, observe that "//depot/BranchTest/Assets/Scenes/SampleScene 1.unity" is "marked for branch in changelist ..." and that "//depot/BranchTest/Assets/Scenes/SampleScene.unity" is "marked for integrate in changelist ..." (use mouseover on the file icons\!)
23. Open the original project in Unity

Expected result: Open for Branch and Open for Integrate are supported in some way by Unity, or at least accurately represented without errors/warnings
Actual result:The following Console messages appear:
"Version Control: invalid p4 stat result: //depot/BranchTest/Assets/Scenes/SampleScene 1.unity"
"Version Control: invalid p4 stat result: //depot/BranchTest/Assets/Scenes/SampleScene 1.unity.meta"

Reproducible with: 2018.4.20f1, 2019.3.7f1, 2020.1.0b4, 2020.1.0a5
Couldn't test wtih 2017.4 (errors)

Notes:
1. If you submit the merge changelist then the correct behavior is observed (the above files are submitted)
2. Assets/Scenes/SampleScene.unity is marked as conflicted which is sort of accurate in that it needs to be resolved. If you do resolve it by accepting the incoming, what happens is the file is locally modified but when you submit the changeset the file remains marked for integrate inside P4V.