I made a test using 22.214.171.124 on an XP machine. In my explanations I will use the terms MASTER PAGE and LAYOUT to make clear which functions I used.
1 - Created 2 presentation with different MASTER PAGES.
2 - Opened Slide Sorter for presentation 1 and 2.
3 - Copied 2 slides from presentation 2 into presentation 1 => MASTER PAGE and LAYOUT copied over into presentation 1
4 - While being in Slide Sorter, applied MASTER PAGE of presentation 1 to slides copied from presentation 2 => immediately saw the change
5 - While being in Slide Sorter, applied LAYOUTs to the copied slides by selecting the copied slides and double clicked on LAYOUTS => I did not see any change in LAYOUT while being in the Slide Sorter.
6 - Changed to Normal View and saw the applied LAYOUTs.
Could it be that you stayed in Slide Sorter and therefore did not see the change in LAYOUT?
As for the availability of slide layouts dialog in the context menu it is not available in my case as well. I used the LAYOUT selection from the sidebar.
Thus you it seems you found 2 bugs. May I propose to file a bug report here: https://www.libreoffice.org/get-help/bug/