Ok, I fixed my problem myself.
Here's what I did:-
1. Uninstalled all Microsoft Visual C++ Redistributables.
2. Instead of downloading them from the official link stated under Requirements in RPH site, I downloaded everything from 2005 to 2022 from this official link and installed them all.
3. I also installed .Net Framework v4.8.1 instead of v4.6.2 from this official link.
4. Restarted system.
Finally, I launched RPH and the launcher ran without any crash and loaded the game with LSPDFR without issue.