Hey there @SgtNelsonUSMC. I want to thank you for pointing out this possible solution. For some mysterious magical reason, my gun stuck animation issue has not been happening after I removed both scripts called "MessageBoards" and the folder for the dlcpacks named "boardpack", which are part of the MessageBoards plugin created by Venoxity. When I removed the plugin ENTIRELY (literally uninstalling everything related to the plugin), my issue has not been replicating since then. I never expected this plugin could possibly be the "main root" of this problem. Of course, this ONLY solved the problem for me temporarily, as I might need to perform more gameplay tests. Yet, whether this plugin affected others and caused this problem as well, it is something I can't confirm. However, from what has happened so far related to this problem as a whole, I can a draw a few conclusions (TL;DR):
1. There might be a high chance that OUTDATED plugins, scripts, or any content that is "additional" a.k.a. mods could be the cause of this problem. Based on what people have experienced so far with this issue, it has happened to individual(s) with or without MODS. Therefore, it can't be 100% confirmed that this problem is only related MODS, but some kind of incompatibilities with functions or tasks that affect the game environment or engine overall. I am not really sure about this, so don't think I am here assuming this is caused because of mods only.
2. If we think about this from a non-modded game perspective, how could this happen even without mods? A very simple answer could be R* updates itself. Since the Christmas update last year, I think there has been a trend related to lots of people reporting this particular issue.
3. This could be unlikely, but could there be a chance that it is not the game itself but something related to the Operating System (OS), or basically Windows could have had some kind of interference with this? I know it sounds vague and ridiculous, but if you think in a broader perspective, there could be a slight chance that Windows updates or computer functionalities (algorithms) could cause this game-breaking glitch. I think this might be a reason because GTA V is more than a decade ago game that has been receiving constant updates indeed, but some functions might have stopped working or became oudated due to new updates that have changed how our PCs process information and data. This is just my theory.
^ Note: Everything stated above is based on my own opinion and theories. No judgment or bias is intended in any of the conclusions.
Thanks.