From an announcement made in the CSSC Discord server:

Hello Sonic Mania runners and community members.

I'm happy to announce that music/SFX mods are now supported for speedrunning! It is a somewhat long process but I tried my best to explain and simplify the steps as much as possible so that anyone can do it. Here is the Google doc tutorial (w/ pictures) for it: https://docs.google.com/document/d/1VLVlHX1EH0tSrJACvkUPkxcQv-cyPcuiF9EokXnyzrE/edit?usp=sharing. If you have any questions or concerns regarding this tutorial then please let me know so I can address them. Before addressing the next thing in this announcement, please note that audio modding is only supported for any version of the game that supports the method described in the document.

Additionally, alongside this tutorial requiring the Mania Mod Manager program to be installed: the 'Disable Background Pausing' function is now officially allowed to be toggled! This can be found under the "Codes" tab at the very bottom of the list. Lastly, I should clarify that all runs on SRC that have used this function in the past will not be affected in any way, due to it having no history of causing any issues for the Mania Mod team regarding verification.

These two additions to the game will be placed under the "Game" rules for both the main and catex pages on SRC.

Be aware that we will be much more vigilant with the usage of mods from this point forward and necessary measures will be taken if we notice any red flags in runs that are submitted. Thank you for reading and have fun audio modding!